The requried, 120 ft³ of water was needed to fill the pool during the summer.
The volume of the child's pool is given by multiplying its length, width, and height.
The volume of the pool = Length x Width x Height
= 5 ft x 4 ft x 2 ft
= 40 cubic feet
Since the pool was filled 3 times during the summer, the total amount of water needed is:
The total volume of water = Volume of pool x Number of times filled
= 40 ft³ x 3
= 120 ft³
Therefore, 120 ft³ of water was needed to fill the pool during the summer.
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pls help QUICK! heres screenshot. 10 points!
Answer:
the answer is (b)
because;
a^2-10a+24
product:24
sum:-10
factor:-6,-4
a(a-6)-4(a-6)
(a-6)(a-4)
therefore:two solutions but only one is given
Three corners of a rectangular city block are located at (2,2), (2,-4) and (-5,-4) on a coordinate plane. What are the coordinates of the fourth corner
Answer:
(-11,8)
Step-by-step explanation:
To find the coordinates of the fourth corner of the rectangular city block, we need to use the fact that opposite sides of a rectangle are parallel and equal in length.
Let's start by finding the length of one of the sides of the rectangle. We can use the distance formula for that:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For example, if we want to find the length of the side between (2,2) and (2,-4), we have:
d = sqrt((2 - 2)^2 + (-4 - 2)^2) = sqrt(6^2) = 6
We can also see from the given coordinates that the sides of the rectangle are parallel to the x or y axis, which means that their lengths are simply the difference between the corresponding x or y coordinates.
So now we know that the length of the sides of the rectangle are both 6 units. The missing corner must be positioned 6 units away from the given point (-5,-4) along the x-axis, since the fourth side of the rectangle is parallel to the x-axis. Therefore, its x-coordinate is -5 - 6 = -11.
Similarly, the fourth corner must be positioned 6 units away from the given point (2,2) along the y-axis, since the fourth side of the rectangle is parallel to the y-axis. Therefore, its y-coordinate is 2 + 6 = 8.
Therefore, the coordinates of the fourth corner are (-11, 8).
Stephan has a box in the shape of a hexagonal prism where the hexagonal bases are regular. A net of the box is below.
In the hexagon diagram, all the sides are drawn with a rectangle on every side and each is added and another hexagon is added to a rectangle.
Note: Figure is not drawn to scale.
He measured the height of the box to be 7 in. Then, Stephan drew a line from the center of one of the hexagons to each of its vertices and noticed that all the triangles he created have a height of 9 in and a base of 10 in.
The geometry of the hexagon is equally divided into six parts of the triangles are shaded inside. The top side is marked as 10 inches, and the length of the triangle is 9 inches.
Note: Figure is not drawn to scale.
What is the surface area of the hexagonal prism?
A.
750 sq in
B.
690 sq in
C.
960 sq in
D.
1,380 sq in
Which statement about congruent arcs is false?
OA. They have the same measure.
B. They are on the same circle or on congruent circles.
C. Their associated chords are perpendicular.
OD. Their associated central angles are congruent.
Answer: Letter C
Step-by-step explanation:
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Since c is saying that congruent arcs associated with chords are perpendicular its wrong.
Solve for the Diameter, X
The measure of the diameter x for the circle is 18.6 units.
A circle is a geometric shape consisting of all points in a plane that are equidistant from a fixed point called the centre. A circle is defined by its radius, which is the distance from the centre to any point on the circle, or by its diameter, which is the distance across the circle passing through the centre and connecting two points on the opposite sides of the circle.
The diameter of a circle is a line segment that passes through the centre of the circle and connects two points on the opposite sides of the circle. The diameter is twice the length of the radius of the circle, and it is often used to express the size or scale of the circle.
The diameter of the circle will be calculated as,
x = 2 ( 3.2 + 6.1)
x = 2 ( 9.3)
x = 18.6 units
Hence, the diameter is 18.6 units.
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What does 96 tell you about the volume of one small cube(1/4)
The larger cube is made up of 384 small cubes, each with a volume of 1/4.
We have,
If we assume that 96 is the total volume of a larger cube made up of smaller cubes, and each small cube has a volume of 1/4.
We can make the following calculation:
Let x be the number of small cubes that make up the larger cube.
The volume of the larger cube = Volume of each small cube x Number of small cubes
96 = (1/4) x
Solving for x.
Multiply 4 on both sides.
96 x 4 = x
x = 384
Therefore,
The larger cube is made up of 384 small cubes, each with a volume of 1/4.
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ASAP NEDDDD HELPPPPPP
By translation, the image of the triangle X is equivalent to the triangle E.
How to determine the image of a figure by rigid transformations
Herein we find the representation of a triangle, whose vertices are described below:
A(x, y) = (5, 5), B(x, y) = (5, 6), C(x, y) = (7, 5)
Whose image must be determined by a rigid transformation known as translation:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Image of the point.T(x, y) - Translation vector.Now we proceed to determine the images of the vertices of the triangle:
A'(x, y) = (5, 5) + (4, - 3)
A'(x, y) = (9, 2)
B'(x, y) = (5, 6) + (4, - 3)
B'(x, y) = (9, 3)
C'(x, y) = (7, 5) + (4, - 3)
C'(x, y) = (11, 2)
Therefore, the triangle E is the image of the triangle X.
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Solve 19×6 using the distributive law.
Answer: (10 * 6) + (9 * 6) = 114
Step-by-step explanation:
Using the distributive property, we can write:
19 × 6 = (10 + 9) × 6
= (10 × 6) + (9 × 6) // Distributive property of multiplication over addition
= 60 + 54
= 114
Therefore, 19 × 6 = 114 when using the distributive law.
Dairy needs 333 gallons of milk containing 6% butterfat. How many gallons of milk containing 7% butterfat and milk containing 4% butterfat must be used to obtain 333 gallons?
222 gallons of milk containing 7% butterfat and 111 gallons of milk containing 4% butterfat must be used to obtain 333 gallons of milk containing 6% butterfat.
Let's assume that x gallons of milk containing 7% butterfat are needed, and y gallons of milk containing 4% butterfat are needed to obtain 333 gallons of milk containing 6% butterfat.
We can set up two equations to represent the given information:
Equation 1: x + y = 333
Equation 2: 0.07x + 0.04y = 0.06(333)
Simplifying Equation 2, we get:
0.07x + 0.04y = 19.98
Multiplying both sides of Equation 1 by 0.04, we get:
0.04x + 0.04y = 13.32
Subtracting this equation from Equation 2, we get:
0.03x = 6.66
Dividing both sides by 0.03, we get:
x = 222
Substituting x = 222 into Equation 1, we get:
222 + y = 333
y = 111
Therefore, 222 gallons of milk containing 7% butterfat and 111 gallons of milk containing 4% butterfat must be used to obtain 333 gallons of milk containing 6% butterfat.
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A cardboard box manufacturing company is building boxes with length represented by x + 1 width by 5-x and height by x-1
The volume of the cardboard box with given dimensions changes at the fastest average rate over the interval of option c. [1,5].
Length of the cardboard box = x + 1
Width of the cardboard box = 5 - x
Height of the cardboard box = x - 1
Volume of the box V (x) = length × width × height
Substitute the values we have,
V(x) = (x+1)(5-x)(x-1)
Expanding this expression gives,
V(x) = -x³ + 5x² + x - 5
To know where Volume is changing at the fastest average rate,
Find the maximum value of the absolute value of the derivative of V(x) over each of the given intervals.
Taking the derivative of V(x), we get,
V'(x) = -3x²+ 10x + 1
Taking the absolute value of this expression, we get,
|V'(x)| = 3x² - 10x - 1
Now, we can calculate the maximum value of |V'(x)| over each interval,
At [1,2]
|V'(1)| = 8
|V'(2)| = 9
[1,3.5]
|V'(1)| = 8
|V'(3.5)| = 0.75
[1,5]
|V'(1)| = 1
|V'(5)| = 24
[0,3.5]
|V'(0)| = 1
|V'(3.5)| = 0.75
The maximum value of |V'(x)| occurs on interval [1,5].
Therefore, the volume of the box is changing at the fastest average rate over the interval option c . [1,5].
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The above question is incomplete, the complete question is:
A cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5 − x, and height by x − 1. the volume of the box is modeled by the function below. over which interval is the volume of the box changing at the fastest average rate?
a. [1,2]
b. [1,3.5]
c. [1,5]
d. [0,3.5]
Enter a positive value for d that makes this statement true: 34×d is less than 34 but greater than zero HELP PLSS FASTT
Answer:
0.5 (any number between 0 and 1)
Step-by-step explanation:
34 * 0.5 = 17
34 > 17 > 0
Rhys takes out a loan of £200, which gathers
interest at a rate of 3% per year. How much
interest will he have to pay after the first year?
Rhys will have to pay £6 interest after the first year.
To calculate the interest, we can use the formula:
Interest = Principal x Rate
Where:
Principal = £200
Rate = 3% = 0.03 (in decimal form)
So, the interest Rhys will have to pay after the first year is:
Interest = £200 x 0.03 = £6
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Jenny has $1200 in her savings account. If the bank pays 3% interest per year on savings, how much interest does she earn in one year?
Answer:
To find out how much interest Jenny earns in one year, we can use the formula:
interest = principal x rate x time
where:
the principal is the amount of money in the savings account
rate is the interest rate per year, expressed as a decimal
time is the length of time the money is in the account, in years
In this case, Jenny's principal is $1200, the rate is 3% or 0.03 as a decimal, and the time is 1 year. Plugging these values into the formula, we get:
interest = 1200 x 0.03 x 1
interest = $36
Therefore, Jenny earns $36 in interest in one year.
Which of the following describes the graph of y--4x-38 compared to the parent square root function?
O stretched by a factor of 2, reflected over the x-axis, and translated 9 units right
O stretched by a factor of 2, reflected over the x-axis, and translated 9 units left
O stretched by a factor of 2, reflected over the y-axis, and translated 9 units right
O stretched by a factor of 2, reflected over the y-axis, and translated 9 units left
Answer:
There is no square root function mentioned to compare with, but assuming you meant the parent square root function y = sqrt(x), the correct answer is:
A.) "stretched by a factor of 2, reflected over the x-axis, and translated 9 units right"
To see this, note that the equation y = 4x + 38 can be rewritten as y - 38 = 4(x - (-9.5)). This means that the graph of y = 4x + 38 is a transformation of the parent function y = sqrt(x) as follows:
It is stretched vertically by a factor of 2 (since the coefficient of x is 4 instead of 1)It is reflected over the x-axis (since the coefficient of x is positive)It is translated 9 units to the right (since the vertex is at (-9.5, -38) instead of (0, 0))So the correct answer is (a) stretched by a factor of 2, reflected over the x-axis, and translated 9 units right.
Answer:
answer is (a) stretched by a factor of 2, reflected over the x-axis, and translated 9 units right.
Step-by-step explanation:
How to find the scientific notation of this problem
Answer:
[tex](4 \times {10}^{4} ) \times (2.5 \times {10}^{6} )[/tex]
[tex] = 10 \times {10}^{10} = {10}^{11} [/tex]
do I mult if x(x+6) m?
The quadratic value equation of triangle area is solved and x = 12 m
Given data ,
Let the triangle be represented as ΔABC
Now , the height of the triangle is h = x m
The base of the triangle is = ( x + 6 ) m
Area of triangle = ( 1/2 ) base x height
A = 108 m² = ( 1/2 ) ( x ) ( x + 6 )
216 = x² + 6x
Subtracting 216 on both sides , we get
x² + 6x - 216 = 0
On factorizing the equation , we get
( x + 18 ) ( x - 12 ) = 0
So , the solution is x = 12 m
Hence , the height of the triangle x = 12 m
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HELP HELP HELP HELP HELP HELPHELP HELP HELPHELP HELP HELPHELP HELP HELPHELP HELP HELP PLS PLE PLS PLS PLs
The answers to the box plot are given as follow;
1) the highest level of snow fall was 50inches. This is the maximum value on the plot
2) The data is most concentrated in the 3rd quarter. More cities has snow fall closer to 40 inches than to 13 inches.
3) the data is most spread all over the 4th quarter.
1) As per the data depicted in a box plot, it can be inferred that no urban center witnesses snowfall exceeding 50 inches.
2) The highest point on this chart supports this observation.
Furthermore, an overwhelming number of cities seem to report moderate levels of snowfall between 13-40 inches as indicated by most of these values lying within that particular section.
To buttress my argument further, I would note how close to its top edge is located the median line for this section. It is apparent that the data exhibits the highest degree of variability during the final quarter, signifying the top 25% of values.
The elongated vertical line extending from the upper end of the box up to the maximum value, which reaches 50 inches, is considerably lengthier than its counterpart at the bottom concluding with a minimum value of 5 inches.
This suggests that there is a greater disparity among snowfall measurements among cities receiving copious amounts.
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20
9
11. The line plot shows the number of miles Elisa ran each week.
a. Choose the appropriate measures to describe the center and
spread of the distribution. Justify your response based on the
shape of the distribution.
b. Write a few sentences describing the center and spread of the
distribution using the appropriate measures. Round to the
nearest tenth if necessary.
3
Miles Ran Each Week
xx---
xx---
8-XXXX
XXXXXX---
XXXX--
--xx
xx---
27 28 29 30 31 32 33 34 35
The distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.
The distribution of miles ran each week by Elisa is relatively symmetric and centered around 30 miles per week, with a relatively tight spread of about 2.3 miles per week.
We have,
a.
Since the distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.
However, the distribution also has some slight right-skewness, so we may want to consider using the median instead of the mean, depending on the context and purpose of the analysis.
b.
The mean of the distribution is:
= (28 + 29 + 30 + 31 + 32 + 33 + 34)/7
= 30.1
So the center of the distribution is around 30 miles per week.
The standard deviation of the distribution is approximately 2.3 miles per week, which tells us that the spread of the distribution is relatively tight.
Alternatively, we could use the median as a measure of the center.
Since there are 7 data points, the median is the average of the 4th and 5th values (30 and 31):
= (30 + 31)/2
= 30.5
So the center of the distribution is also around 30 miles per week using the median.
Thus,
The distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.
The distribution of miles ran each week by Elisa is relatively symmetric and centered around 30 miles per week, with a relatively tight spread of about 2.3 miles per week.
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The normal curve represents a distribution where the
are equal to each other.
a. range/ standard deviation/variance
b. mean/median/standard deviation
c. mode/median/standard deviation
d. mean/median/mode
and
The normal curve represents a distribution where the mean, median, and mode are equal to each other.
What does normal curve represents a distribution where the are equal to each other?The normal curve denotes a distribution in which the mean, median, and mode are all equal. As a result, the right answer is:
The curve of a normal distribution is symmetrical and bell-shaped, with the mean, median, and mode placed in the center. The standard deviation is a measure of the data's spread or dispersion around the mean.
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For the function h(y)=4|y+2|−3, evaluate h(−8).
Answer: h(-8) = 21
Step-by-step explanation:
Answer: 21
Step-by-step explanation:
You equation is h(y) but you need to find h(-8) which means substitute y for -8 into equation
h(-8)= 4|(-8)+2| -3 do what's inside absolute value first
=4|-6| -3 for absolute value, take positive of number
=4(6)-3 multiply
=24-3 subtract
=21
Can someone please help me with this? I'm struggling and it's already late :(
Answer:
(2, -5)
(4, -3)
(3, -1)
Step-by-step explanation:
When reflected across the X-axis, the sign of the y will change to the opposite.
(x, y) → (x, -y)
Let's solve
(2,5) → (2, -5)
(4,3) → (4, -3)
(3,1) → (3, -1)
So, the missing coordinates are: (2, -5)
(4, -3)
(3, -1)
What is the smallest positive integer n such that the fourth root of 56*n*360 is an integer?
The smallest positive integer n that makes the fourth root of 56n360 an integer is n = 81.
We can start by simplifying the expression inside the fourth root:
56 * n * 360 = [tex]2^{3}[/tex] * 7 * n * [tex]2^{3}[/tex] * [tex]3^{2}[/tex] * 5
= [tex]2^{6}[/tex] * [tex]3^{2}[/tex] * 5 * 7 * n
Taking the fourth root of this expression gives:
[tex](56*n*360)^{(1/4)}[/tex] = [tex](2^{6}*3^{2}*5*7*n) ^{(1/4)}[/tex]
= [tex]2^{(6/4)}[/tex] * [tex]3^{(2/4)}[/tex] * [tex]5^{(1/4)}[/tex] * [tex]7^{(1/4)}[/tex] * [tex]n^{(1/4)}[/tex]
= 4 * [tex]3^{(1/2)}[/tex] * [tex]5^{(1/4)}[/tex] * [tex]7^{(1/4)}[/tex] * [tex]n^{(1/4)}[/tex]
For the fourth root to be an integer, [tex]n^{(1/4)}[/tex] must be an integer, and since we want n to be as small as possible, we want [tex]n^{(1/4)}[/tex] to be as small as possible.
The smallest possible value of n that makes [tex]n^{(1/4)}[/tex]an integer is when n is a fourth power of a prime number. Therefore, we can let n = [tex]p^{4}[/tex], where p is the smallest prime number that makes the expression under the fourth root an integer.
From the expression above, we can see that p must be a factor of 7 and [tex]35^{2}[/tex] in order to make the expression under the fourth root an integer. The smallest prime factor of 7 and [tex]35^{2}[/tex] is 3, so we can let p = 3. Then:
n = [tex]p^{4}[/tex] = [tex]3^{4}[/tex] = 81
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In XYZ, /Y=83°, XY =9, and XZ= 10. To the nearest tenth, what is /z?
The angle of Z is 63.2 degree.
Isosceles Triangle:The word isosceles comes from the Ancient Greek term isosceles which literally means "equal-legged." An isosceles triangle has two of its sides of equal length, which means that the angles opposite these sides would also be of equal measure.
In Triangle ΔXYZ,
∠Y = 83°, XY = 9 and XZ = 10
To find the angle of Z
Using Sine rule :- sine rule relates the sine of each angle to length of opposite side.
[tex]\frac{Sin A}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]
Where, A, B , C are the angles of the triangles and a, b, c are the side of the triangles
Then, Apply it:
[tex]\frac{Sin83}{10}=\frac{SinZ}{9}[/tex]
Using cross multiplication:-
Sin 83 × 9 = Sin Z × 10
Sin Z = (Sin 83 × 9)/10
Sin Z = 0.893
∠Z = [tex]Sin^-^1(0.893)[/tex]
∠Z = 63.2°
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To rent a certain meeting room, a college charges a reservation fee of $18 and an dditional fee of $4 per hour the chemistry club wants to spend less than $50 on renting the room. possible number of hour the chemistry club could rent the meeting room?
use t for the number of hours.
write your answer as an inequality. solved for t
t < 8 is the inequality to solve the variable "t" as per the given data.
The cost C (in dollars) of renting the room for t hours can be expressed as:
C(t) = 4t + 18
To spend less than $50, we can set up an inequality:
C(t) < 50
Substituting the expression for C(t), we have:
4t + 18 < 50
Subtracting 18 from both sides, we get:
4t < 32
Dividing both sides by 4, we obtain:
t < 8
Therefore, the chemistry club could rent the meeting room for any number of hours less than 8 in order to spend less than $50.
The inequality solved for t is:
t < 8
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1 pound = 1.20
Euros
If one pound 1.2 euros then 14 pounds is 21 euros.
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity
Given that 1 pound is 1.2 euros
We have to find 14 pounds in euros
To do this we just need to multiply 14 with 1.2
14×1.5
21 euros
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Please help. This is due and I don't know how to solve it.
Answer:for the one in the middle, that one is 5.0, for the one in the top, that one is 7, and for the bottom one, that one is 50
Step-by-step explanation:
Determine if the question is a Statistical Question
Answer:
jordans van
Step-by-step explanation:
yes satiscal
Offering 100 points to the first correct answer. Need asap, please!
A rectangle has sides measuring (6x + 4) units and (2x + 11) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Expression used for area of a rectangle is 12x² + 74x + 44 .
Its degree and classification is 2 and quadratic
and demonstration of a closure property is given by product of a polynomial is a polynomial.
Length of the rectangle = (6x + 4) units
and Width of the rectangle = (2x + 11) units.
The area of the rectangle is given by the product of its length and width,
Area = (6x + 4) × (2x + 11)
Find the product,
⇒ Area = 6x × 2x + 6x × 11 + 4 × 2x + 4 × 11
Simplifying this expression, we get,
⇒ Area = 12x² + 74x + 44
The expression that represents the area of the rectangle is 12x² + 74x + 44.
The degree of the expression 12x² + 74x + 44 is 2,
since the highest power of x is 2.
The classification of this expression is quadratic.
Part A demonstrates the closure property for polynomials because the product of two polynomials is also a polynomial.
Here, the area of the rectangle is the product of two polynomials (6x + 4) and (2x + 11).
And the result is also a polynomial (12x² + 74x + 44).
This shows that the set of polynomials is closed under multiplication.
Which is one of the defining properties of a mathematical system.
Therefore, the expression for area of a rectangle is (12x² + 74x + 44) ,
Degree and classification is 2 and quadratic and closure property is demonstrate by product of a polynomial.
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A parachutist's rate during a free fall reaches 165 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Rate: m/s
Distance fallen in 5 seconds: m
In 5 seconds of free fall at a speed of 165 feet per second, the parachute user will drop around 122.5 meters.
To convert feet per second (ft/s) to meters per second (m/s), we can use the following conversion factor:
1 m/s = 3.3 ft/s
Therefore, the parachutist's rate of 165 ft/s is equivalent to:
165 ft/s × (1 m/3.3 ft) = 50 m/s
Next, we can use the kinematic equation:
d = 1/2 * a * t²
Here d is the distance traveled (in meters), a is the acceleration due to gravity (9.8 m/s²), and t is the time (in seconds).
For 5 seconds of free fall, we have:
d = 1/2 * 9.8 m/s² * (5 s)² = 122.5 m
Therefore, the parachutist will fall approximately 122.5 meters during 5 seconds of free fall at a rate of 165 ft/s.
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The volume of a cylinder is 637 cm³. If the radius is 3 cm, what is the height
of the cylinder?
If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:
637 = π(3²)h
Simplifying:
637 = 9πh
h = 637 / (9π)
h ≈ 7.06
Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.
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