A cone fits inside a square pyramid as shown. For
every cross section, the ratio of the area of the circle to
Since the area of the circle is the area of the
square, the volume of the cone equals
the area of the square is
or 7
402
o the volume of the pyramid or - Alenchor
arh.
Cross section
r
o the volume of the pyramid or
+(1200)
2n.
o the volume of the pyramid or z { nºm) or
7
2r
2r
22h.
0 Į the volume of the pyramid or = { 29°m) oraz
arh.
m no
Answers
The volume of the cone is [tex]\frac{\pi}{4}[/tex] the volume of the pyramid
The ratio of the area is given as:
[tex]R= \frac{\pi r^2}{4r^2}[/tex]
or
[tex]R= \frac{\pi}{4}[/tex]
The volume of a cone is:
[tex]V_1 = \frac 13 \pi r^2 h[/tex]
For a pyramid, the volume is:
[tex]V_2 = \frac 43 r^2h[/tex]
Rewrite as:
[tex]V_2 = 4 * \frac 13 r^2h[/tex]
Divide by 4
[tex]\frac{V_2}{4} = \frac 13 r^2h[/tex]
Substitute [tex]\frac{V_2}{4} = \frac 13 r^2h[/tex] in [tex]V_1 = \frac 13 \pi r^2 h[/tex]
So, we have:
[tex]V_1 = \frac{V_2}{4} * \pi[/tex]
This gives
[tex]V_1 = \frac{\pi}{4} V_2[/tex]
Hence, the volume of the cone is [tex]\frac{\pi}{4}[/tex] the volume of the pyramid
Read more about volumes at:
https://brainly.com/question/9554871
Related Questions
Jackie has a puzzle book that contains a total of 70puzzles she has completed 2/5 of the puzzle in the book if Jackie completes 18 more puzzles what is the total number of puzzles that she will has completed in the book ?
Answers
Answer: 46 puzzles
Step-by-step explanation:
There are 70 puzzles in total in the book.
Jackie has completed 2/5 of these puzzles which is:
= 2/5 * 70
= 28 puzzles
Jackie has completed 28 puzzles. She then completes 18 more. The total number of puzzles completed is:
= 28 + 18
= 46 puzzles
Will spent $40 at the fair. It cost $20 to get in the fair and $0.50 per ticket to ride the rides. How many tickets did Will buy? A. 40 B. 20 C. 120 D. 30
Answers
Answer:
B.20
Step-by-step explanation:
10. Which equations could be used to solve
for x? Circle all that apply.
Answers
Answer: B and D
Step-by-step explanation:
Miranda opened a checking account with $560 from her summer job. She
withdrew the same amount each week for 13 weeks. Her balance was then
$365. Solve the equation 560 - 13m = 365 to find how much money m she
withdrew each week.
Answers
Answer:
The answer is $15.00 :)
Step-by-step explanation:
I took the test and that was the correct answer I got for this problem
A construction worker drops a hammer from 25m. How long will it take for the hammer to hit the ground? H(t)= -4.9t^2 +v +h
Answers
Answer:
the time taken for the hammer to hit the ground is 2.26 s.
Step-by-step explanation:
Given;
height through which the hammer falls, h = 25 m
The time taken for the hammer to hit the ground is calculated as;
[tex]h(t) = ut + \frac{1}{2} gt^2\\\\h(t) = 0 + \frac{1}{2} (9.8)t^2\\\\h(t) = 4.9t^2\\\\t = \sqrt{\frac{h(t)}{4.9} } \\\\t = \sqrt{\frac{25}{4.9} } \\\\t = 2.26 \ s[/tex]
Therefore, the time taken for the hammer to hit the ground is 2.26 s.
hii please help i’ll give brainliest!!
Answers
Answer:
very top
Step-by-step explanation:
i had a test on it a week ago
pls give brinliest
Find the probability that you will roll an even number exactly 5 times when you:
roll a six-sided number cube 10 times.
P =0.246
roll a six-sided number cube 20 times.
P =0.015
Explain why the second result is less.
Answers
Please mark brainliest would greatly be appreciated.
Answer:
Sample Response: As the number of trials changes, the distribution changes. Since there is a 50% chance of rolling an even number, having a small number of successes is less likely when the number of rolls increases.
Step-by-step explanation:
I just did the Assignment on EDGE2020 and it's 200% correct!
Also, heart and rate if you found this answer helpful!! :) (P.S It makes me feel good to know I helped someone today!!) :)
NEED HELP ASAP|!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
thanks for freepoints
have q nice dayyyyy
love youuuuuuuuuuhope all your dreams come true
hahahahahahahahahah
In the following figure, the value of xs is
20
35
Answers
Where's the figure?
∝ Sidhdi
Translate the description as an algebraic expression:
a multiplied by the cube of 15
Answers
Answer:
t's no big surprise that variables act like pronouns, because (believe it or not) math is basically its own language, defined by numeric and logical rules. Therefore, one of the first skills you must master is how to translate regular English into this new (much geekier) math language. For now, I will help you translate English phrases into mathematical phrases, called
Step-by-step explanation:
Answer:
or
a(3375)
Step-by-step explanation:
You are multiplying a by the cube of 15
15 cubed = [tex]15^{3}[/tex] = 3375
Help please due in in 10 minutes
Answers
Answer:
answer is G
zeros are 3, -5
brainlist if you get this right please :)
help pls will get brainlest
Answers
Step-by-step explanation:
the answer to your question is
a
Answer:
54 inches squared.
Step-by-step explanation:
(6*3) + (6*3) + (3*3) + (3*3). The areas of the faces added together. It is basically the perimeter of a 3D shape, except instead of measuring 2D sides, it is 3D shaped faces.
George solved the following system of equations using substitution.
y = 4.3 – 21
12x – 3y = 63
He decided there is no solution. After the following steps:
y= (4x – 21)
12x - 3(4x – 21) = 63
12:- 12.c + 63 = 63
63 = 63
Is George correct in his conclusion? If not choose the correct solution below. If he is correct, select that choice.
A) George is correct with no solution.
B) He is not right. There are infinitely many solutions.
C) He is not right. The solution is (63,63)
Answers
Answer:
B
Step-by-step explanation:
-4x + y = -21
12x -3y = 63
-4/12 = -1/3
1/-3 = -1/3
-21/63 = -1/3
If we graph the two lines, we can discover that are the same, so they have infinite points in common
Felipe calculated that he uses about 545 gallons of fuel each year. His car's owner's manual says that it is approved to use regular fuel. How much money can he save each year by switching from premium fuel, at $4.59 per gallon, to regular fuel at $4.18 per gallon?
$0.41
$2,501.55
$223.45
$2,278.10
$4,779.65
Answers
Answer:
$223.45
Step-by-step explanation:
premium fuel: 4.59 x 545
= 2501.55
regular fuel: 4.18 x 545
=2278.1
2501.55-2278.1 = 223.45
is x+y=3 and x+y=7 a one solution, no solution, or an infinitely many solution
Answers
Answer:
No solution
Step-by-step explanation:
The lines are parallel because they have the same slope.
Elimination method also just gives you 3 = 7 which is not true, therefore no solutions.
30% of what number is 7.5?
Answers
Five whole numbers are written in order.
4
7
x
y
11
The mean and median of the five numbers are the same.
Work out the values of
x
and
y
.
(3 marks)
Answers
Answer:
The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.
The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115
Step-by-step explanation:
The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.
The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.
The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.
The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115
Problem
3. The diagram shows the distance a tortoise can
walk if it walks at a constant pace for 15
minutes. At the same rate, how many
kilometers can the tortoise walk in 1 hour?
Write your answer as a decimal.
Minutes H
0
15
Meters
+
400
0
Answers
Explanation is in the file
tinyurl.com/wpazsebu
if i have 9,999 points and divide that by 33 then subtract that by 99 and then add 738 how much will i have left lol
Answers
Answer:
942
Step-by-step explanation:
Answer:
942
Step-by-step explanation:
9999 divided by 33 equals 303
303 minus 99 equals 204
204 plus 738 equals 942
trigonometry please help! work need to be shown
Answers
Answer:
6.13
Step-by-step explanation:
This diagram shown is a right triangle;
USing the SOH CAH TOA idenity
Adjacent = x
Hypotenuse = 8
Angle of elevation = 40 degrees
cos theta = adj/hyp
cos 40 = x/8
x = 8cos40
x = 6.13
Hence the value of x to the nearest hundredth is 6.13
Which pairs of fractions are equivalent? Mark all that apply. 4/5 and 8/12 2/3 and 10/15 1/6 and 3/18 2/7 and 6/20
Answers
Answer:
2/3 and 10/15 1/6 and 3/18
Step-by-step explanation:
to determine which fractions are equivalent, we multiply each fraction by 100
4/ 5 x 100 = 80
8/12 x 100 = 66.67
4/5 and 8/12 are not equivalent
2/3 x 100 = 66.7
10/15 x 100 = 66.7
2/3 and 10/15 are equivalent
If 10/15 is expressed in its simplest form. that is if both numerator and denominator are divided by 5, it would equal 2/3
1/6 x 100 = 16.7
3/18 x 100 = 16.7
1/6 and 3/18 are equivalent
If 3/18 is expressed in its simplest form. that is if both numerator and denominator are divided by 3, it would equal 1/6
2/7 x 100 = 28.6
6/20 x 100 = 30
2/7 and 6/20 are not equivalent
23.3238 rounded to the nearest hundreath
Answers
Answer:
23.32
Step-by-step explanation:
the hundredths place is the 2 spot after the decimal
and if the # to the right of that # is 5 or grater you add a one
if it is 4 or lower you keep the # the same
23.3238
because 3 is next to the second place the 2 just stays the same
so now it's
23.32
1. Sketch the graph of f(x) = 3* and describe the end behavior of the graph.
id
X
8
6
-2
4
-1
I
2
0
-10-9-8-7 -6 -5 -4 -3 -2 -1 10
0
2.
3 4 5 6 7 8 9 10
o
-2
1
-4
2.
-6
-8
Answers
Find the value of x. Show your work.
Answers
Answer:
54=x
Step-by-step explanation:
90=43+(x-7)
47=x-7
54=x
symbolab is great for math equations btw
Can somebody please help me out with this question? Asap
Answers
A. Simplify x + 8 to 8x.
Jeremy and his classmates conduct an experiment with a set of weights and a spring. They record their results in the table.
Use the table to answer Items 21-24.
2
Student
Mass (lb)
Spring Stretch (in.)
Jeremy
5
7.5
Adele
I
12
Roberto
14
21
Shanice
21
36
Guillaume
28
42
21. Make a graph of the data.
Answers
Here's link to the answer:
tinyurl.com/wpazsebu
Help me with this plz.....???????????????!?????!!!!!!!
Answers
Answer:
Check pdf
Step-by-step explanation:
URGENT, PLEASE ANSWERR If someone who is 5 feet tall uses a potato gun to shoot a potato in the air at 100 feet per second, we can use the function ℎ()=−162+100+5 to calculate how far the potato will be from the ground at any given second (t). What does the h(0) represent in the context of the problem?
Answers
Given:
Consider the function is:
[tex]h(t)=-16t^2+100t+5[/tex]
This function is used to calculate how far the potato will be from the ground at any given second (t).
To find:
The value of h(0) and its meaning in the context of the problem.
Solution:
We have,
[tex]h(t)=-16t^2+100t+5[/tex]
At t=0,
[tex]h(0)=-16(0)^2+100(0)+5[/tex]
[tex]h(0)=0+0+5[/tex]
[tex]h(0)=5[/tex]
Therefore, the value of h(0) is 5. It means the potato is 5 feet from the ground at the time of shooting.
The lengths of the sides of the triangle are 13cm, 14 cm, and 15 cm. Is the triangle a right triangle?
Yes or No?
Show your work to receive brainliest! (lots of points)
Answers
Answer:
No, it is not a right triangle.
Step-by-step explanation:
If the triangle was a right triangle, then the Pythagorean Theorem states that a^2 + b^2 = c^2. Let's test it on this triangle:
13^2 + 14^2 = 365, or c^2. If this is a right triangle, c should equal 15.
However, sqrt(365) = 19.1, which is not 15. So, the triangle is not a right triangle.
How do you graph it ?
Answers
Answer:
It should look like this
Step-by-step explanation:
hope it helps