In the right hexagonal pyramid below. The hexagonal base is regular and has sides that are 8 units long. The altitude of the pyramid is 18 units. Determine the volume of the pyramid to the nearest cubic unit.

Answers

Answer 1

Answer:

The volume is 997.62 cubic units..

Step-by-step explanation:

We are given the following details:

The pyramid has a regular hexagonal base i.e. each side of hexagon is equal.

Side of hexagonal base, a = 8 units

Altitude of pyramid, h = 18 units

We have to find the volume of pyramid.

Formula:

[tex]V = \dfrac{1}{3} \times B \times h[/tex]

Where, B is the area of base of pyramid.

h is the height/altitude of pyramid

To calculate B:

Here, base is a hexagon with side 8 units.

[tex]\text{Area of hexagon, B }= 6 \times \dfrac{\sqrt{3}}{4}a^{2}[/tex]

Here, a = 8 units

[tex]\Rightarrow B = 6 \times \dfrac{\sqrt{3}}{4}\times 8^{2}\\\Rightarrow B = 166.27\text{ square units}[/tex]

Putting values of B and h in Formula of volume:

[tex]\Rightarrow V = \dfrac{1}{3} \times 166.27 \times 18\\\Rightarrow V = \dfrac{2992.89}{3} = 997.62\text{ cubic units}[/tex]

Hence, the volume is 997.62 cubic units.


Related Questions

my entry test is coming soon i prepard my exams maths english

Answers

Answer:

good luck !!

Step-by-step explanation:

Answer:

Good luck

Step-by-step explanation:

Jessica has 4/8 of a bottle of Robitussin syrup on hand. The pharmacist instructs Jessica to reduce the syrup by 1/2 so he can prepare a patient’s prescription. How much Robitussin does the pharmacist need to prepare the prescription?

Answers

Answer:

2/4 i think but im not sure

Isi makes sandwiches to sell at a football game.
The graph shows her costs and income from making and selling the sandwiches.

Select the three statements that are true, based on the graph.

Answers

Answer: 1)The more sandwiches you sell the more you income goes up. 2)If you sell 24 sandwiches  the cost will be the same as your income. 3) If you sell 0 sandwiches you will get zero income.

Step-by-step explanation:

Rearrange the equation so m is the independent variable.

-2m-5n=7m-3n

n = __

Answers

Answer:n=-9/2m

Step-by-step explanation:

Step 1: Add 3n to both sides.

-2m-5n+3n=7m-3n+3n

-2m-2n=7m

Step 2: Add 2m to both sides.

-2m-2n+2m=7m+2m

-2n=9m

Step 3: Divide both sides by -2.

-2m/-2=9m/-2

n=-9/2

Hope I helped

Answer:

n= -9m/2

Step-by-step explanation:

-2m-7m-5n=7m-7m-3n

-9m-5n+5n= -3n+5n

-9m=2n

n= -9m/2

A cylinder is 20 inches long and has a diameter of 10 inches. What is the approximate volume of the cylinder?

Answers

Answer:

V=π(d/2)^2·h

=π·(10/2)^2 · 20

≈1570.79633in³

this is the correct answer!!!

The approximate volume of the cylinder is 1570.796 inches³.

What is Volume?

Volume of a three dimensional shape is the space occupied by the shape.

A cylinder is a geometrical shape has two circular bases which are parallel and they are connected with a curved surface.

Given that,

Height of the cylinder = 20 inches

Diameter of the base = 10 inches

Radius = Diameter / 2 = 10/2 = 5 inches

Volume of the cylinder = π r² h, where r is the radius and h is the height.

Volume = π (5)² (20)

             = 500π

             = 1570.796 inches³

Hence the volume is approximately 1570.796 inches³.

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A circular swimming pool has a radius of 15ft. There is a path all the way around that pool that is three feet wide. What is the circumference of the outer edge of the path around the pool? Use 3.14 for pie

Answers

Answer:

94.2 ft.

Step-by-step explanation:

The equation to find circumference is 2 times pie times radius. We subsitute  pie for 3.14. Now the equation is 2(3.14)r. The radius is 15. When we subsitute 15 for r the answer will be 2(3.14)15. Another way to write it is 2 times 3.14 times 15. The answer would be 94.2

Identify the opposite of -4

Answers

Answer:

It is 4

Step-by-step explanation:

The diameter of this beach ball is 12 inches.

A beach ball.

Apply the formula for the volume of a sphere to determine how much air it can hold. Use the calculator to multiply by π. Round to the nearest hundredth.

Sphere V = 4
3
πr3

How much air can the beach ball hold?

Answers

Answer:

288π or 904.78

Step-by-step explanation:

We know that the diameter of this beach ball is 12 inches and we want to determine how much air it can hold using the formula for the volume of a sphere which is [tex]\frac{4}{3}[/tex] × π × r³ where 'r' is the radius. In the question we are given the diameter not the radius but we can half the diameter to find the radius so 12 ÷ 2 = 6. The radius of the beach ball is 6 inches so let's work out how much air it can hold.

Volume = [tex]\frac{4}{3}[/tex] × π × r³

→ Let's substitute in the values

Volume = [tex]\frac{4}{3}[/tex] × π × 6³

→ Simplify

Volume = [tex]\frac{4}{3}[/tex] × π × 216

→ Simplify further

Volume = 288π or 904.78

The amount of air can the sphere shape beach ball hold is 208π or 904.78 inches.

What is sphere?

The "set of all  points  in 3 dimensional space is lying the same distance from the given points or center" is called sphere.

According to the question,

Diameter of sphere shape beach ball is 12inches

Radius of sphere shape beach ball is 12/2 = 6inches

Volume of sphere = [tex]\frac{4}{3}[/tex] × π × r³  

= [tex]\frac{4}{3}[/tex] × [tex]\frac{22}{7}[/tex] × (6)³

= 904.78inches

Hence, the amount of air can the sphere shape beach ball hold is 208π or 904.78 inches.

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Solve for m.

774 = m − 15

Answers

Answer:

[tex]m = 789[/tex]

Step-by-step explanation:

[tex]774 = m - 15 \\ 774 + 15 = m \\ 789 = m[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

So the right answer is 789

look at the attached picture

Hope it will help you

Good luck on your assignment

( NEED HELP ASAP)

If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?

[Hint: Place your coordinates in the blank with no parentheses and a space after the comma in the form: x, y]

Parallelogram ABCD is shown.
A is at negative 4, 1.
B is at negative 3, 2.
C is at 0, 2.
D is at negative 1, 1.

Answer:

(Fill in the blank)

Answers

Answer:

  A' is at (-4, 1)

Step-by-step explanation:

Reflection over both axes is equivalent to rotation by 180°. Then rotation by 180° returns the point to its original location. The original location of point A is (-4, 1), so the location of its image is A'(-4, 1).

p + nx=rx-e (solve for x)

Answers

Answer:

(p+e)/(r-n) =  x

Step-by-step explanation:

p + nx=rx-e

Add e to each side

p +e+ nx=rx-e+e

p +e+ nx=rx

Subtract nx from each side

p +e+ nx - nx=rx-nx

p+e = rx -nx

Factor out x

p+e = x(r-n)

Divide each side by (r-n)

(p+e)/(r-n) =  x(r-n)/(r-n)

(p+e)/(r-n) =  x

How do I solve the problem?

Answers

You have to determine how many weeks it takes them to make that much, then you add the total. you can determine how many weeks it takes by multiplying

Answer: So you have to first find out how many weeks Alicia needs to work and write it like this (an example)

3x?=9 something like that hope i helped

Step-by-step explanation:

What is 4+5 devices by two

Answers

The equation can be written as:

4 + 5 / 2

Remember to follow PEMDAS.

4 + 5 / 2

4 + 2.5

6.5

Best of Luck!

Answer:

If you mean whats 4+5/2 the answer is 6.5 because PEMDAS says to Divide first . So 4+(5/2). 5/2 is 2.5. so 4+(2.5) which equals 6.5

I need Help..please??

Answers

Answer:

56

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

If f(x) = 5 + 4x^2, then f(3) =
. Give only the final answer

Answers

[tex]\text{Solve by plugging in 3 to x:}\\\\f(x)=5+4(3)^2\\\\f(x)=5+4(9)\\\\f(x)=5+36\\\\f(x)=41\\\\\boxed{f(3)=41}[/tex]

Answer:

hope this helps

Step-by-step explanation:

f(x) = 5 + 4x^2, then f(3)

5 + 4(3)^2

5+4(9)

5+36

41

om is 5 years younger than his brother. If the sum of their ages is 43 years now, find their age.

Answers

Answer:

Brother's age =24

Om's age =19

Step-by-step explanation:

Let bro's age be x

Let om's age be x-5

x+x-5=43

2 x -5=43

2 x = 43+5

2 x = 48

x = 24

In the equation -2 - 6b = 32, the negative coefficient is ___________________.

Answers

Answer:-2

Step-by-step explanation:

It’s not -6b because that is showing that it’s getting subtracted

Hope I helped

When playing roulette at the Venetian casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 27 or to bet $5 that the outcome is any one of these five possibilities: 0, 00, 1, 2, 3. From Example 6, we know that the expected value of the $5 bet for a single number is -26. For the $5 bet that the outcome is 0, 00, 1, 2, or 3, there is a probability of 5>38 of making a net profit of $30 and a 33>38 probability of losing $5.
a. Find the expected value for the ​$5 bet that the outcome is 00, 0, or 1.
b. Which bet is​ better: a $5 bet on the number 25 or a $5 bet hat the outcome is any one of the numbers 00, 0, or 1? Why?

Answers

Answer:

Step-by-step explanation:

Given that:

To bet $5 that the outcome is any one of these five possibilities: 0, 00, 1, 2, 3.

Let Y represent the Amount of net profit

Then, Y= {-5, 30}

The probability distribution of Y is:

Y                        -5                        30

P(Y=y)                [tex]\dfrac{33}{38}[/tex]                        [tex]\dfrac{5}{38}[/tex]

a)  The expected value of X is given by:

[tex]E[Y] =\sum y P(Y=y)= 30*\dfrac{5}{38}-5*\dfrac{33}{38}[/tex]

[tex]=-0.39[/tex]

[tex]= -39 \ cents[/tex]

b)

On a bet of $5 on the number 25 we are expected to loose 24 cents.

While on a $5 bet that the outcome is any one of the numbers 0,00, or 1 we are expected to loose 39 cents.

Hence,  $5 bet on the number 27 is better. Because the expected loss is less in this bet

ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.

Answers

Answer:

X is 108, infinite

Step-by-step explanation:

An insurance policy charges a regular risk premium, , at Years 0,1,2,3,…,9 from today. The policy pays a claim of 2 (i.e. × ) in 15 Years from today. Calculate the value of (to 2 decimal places), assuming an interest rate of 2% per annum.

Answers

Answer:

x = 12.29

Step-by-step explanation:

present value of the claim = x² / (1 + 2%)¹⁵ = 0.743x²

present value of the 10 premiums:

x + x/1.02 + x/1.02² + x/1.02³ + x/1.02⁴ + x/1.02⁵ + x/1.02⁶ + x/1.02⁷ + x/1.02⁸ + x/1.02⁹ = x + 0.9504x + 0.9612x + 0.9423x + 0.9238x + 0.9057x + 0.888x + 0.8706x + 0.8535x + 0.8368x = 9.1323x

0.743x² = 9.1323x

x² / x = 9.1323 / 0.743

x = 12.29

Answer

x = 12.29

Step-by-step explanation:

Given that the policy claims x² in 15 years, at 2% = 0.02, the present value of the claim is given as:

x²/(1 + 0.02)^15

= x²(1/1.02)^15

= 0.743x²

The present value of the 10 premiums:

x + x/1.02 + x/1.02² + x/1.02^3 + x/1.02^4 + x/1.02^5 + x/1.02^6 + x/1.02^7 + x/1.02^8 + x/1.02^9

= x + 0.9504x + 0.9612x + 0.9423x + 0.9238x + 0.9057x + 0.888x + 0.8706x + 0.8535x + 0.8368x

= 9.1323x

Now,

0.743x² = 9.1323x

x²/x = 9.1323/0.743

x = 12.29

This is what we are looking for.

Which of the following shows the division problem below in synthetic division form? 4x^2-13x+8 / x+5

Answers

Answer:

Dividing 4x^2 - 13x + 8  by x + 5 or x - (-5), in synthetic division form:

-5)        4          |       -13      |          8

           ↓               4 x (-5)     (-5) x (-33)  

           4                 -33               173

=> Quotient is 4x - 33 and remainder is 173

=> (4x^2  - 13x + 8)/(x + 5) = (4x - 33) + 173/(x + 5)

Hope this helps!

:)

Answer:

-5/4 -13 8

Step-by-step explanation:

Based on the information marked in the diagram mnp and qrs must be congruent

Answers

Answer: True

Step-by-step explanation:

In triangles MNP and QRS:

NP=RS (hypotenuses);

∠P=∠S (acute angles).

Then, triangles MNP and PRS are congruent by HA theorem.

which makes the answer true

Answer:

True

Step-by-step explanation:

I just took the test, A-p-e-x

can someone help me answer the pic above

Answers

Answer:

The cop = 40 and the baseball cap = 3 and the baseball bat = 21

Step-by-step explanation:

So 40 - 21 + 3(2) = 25

Answer:

25

Step-by-step explanation:

look at the whole thing first. you see that the field = player so first you do 120/3. you get 40. then for teh second you have two "40's" and an unknown. so you do 101-80 because 40+40=80 and get 21. for the fourth you have 21/?=7 . we can do 21/7=3 to find this. so the helmet is 3. for the final we have 40-21+6 and that equals 25. thank you ;)

magine that you are conducting a one-variable chi-square test to investigate the hypothesis that there are equal numbers of cat lovers and dog lovers in the office at work. Having conducted a survey, you found 150 preferred dogs and 120 preferred cats. What would the expected frequencies be in each cell? 135 150 and 120 270 More information is needed to calculate the expected frequencies.

Answers

Answer:

a. 135 is correct

Step-by-step explanation:

We have the following information:

dogs lover: 150

cats lover: 120

as the null hypothesis:

H, there are equal number of dogs lover and cats lover, so the expected frequency in each cell will be equal and that is:

f = (150 + 120) / 2

f = 270/2 = 135

so option a. 135 is correct

There are 7 x 104 snakes at the zoo but 7 x 100 are accounted for. How many snakes are missing.

Answers

Answer:

28 snakes are missing

Step-by-step explanation:

7 times 104 = 728

7 times 100 = 700

728 minus 700 = 28 snakes are missing

The volume of a sphere is 904.32 cubic millimeters. What is its radius?

Answers

Hello!

Answer:

[tex]\boxed{ \bf The~radius~of~the~sphere~is~6~mm.}[/tex]

Explanation:

We know that:

V = [tex]\frac{4}{3}[/tex]πr³

904.32 = [tex]\frac{4}{3}[/tex]πr³

To figure out the radius, we have to undo the above. We can undo the fraction by multiplying by it's reciprocal:

[tex]\frac{3}{4}[/tex] × [tex]\frac{904.32}{1}[/tex] = [tex]\frac{4}{3}[/tex]πr³ × [tex]\frac{3}{4}[/tex]

678.24 =  πr³

Next, we're going to divide both sides by pi:

[tex]\frac{678.24}{\pi } = \frac{\pi r^{2} }{\pi }[/tex]

215.90 = r³

To undo the, we must find the cube root of 215.90.

r = 6

Answer:

[tex]radius = 6mm[/tex]

Step-by-step explanation:

Volume of a sphere.

Use this formula

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

Now solve for r

[tex]r = (3 \frac{v}{4\pi} ) ^{ \frac{1}{3} } \\ = (3 \times \frac{904.32}{4 \times \pi} ) ^{ \frac{1}{3} } \\ ≈

5.99899mm

[/tex]

The circumference of a circle is 20 cm. What is the approximate radius of the circle?

Answers

Answer:

[tex]3.18cm[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

if the product of 11 positive integers is odd, how many of these integers must be odd

Answers

If u can’t find the answers on here you can always try using the Socratic app

I need help please and thank you

Answers

Answer:

  2.2×10⁹

Step-by-step explanation:

The distributive property is useful here. Recognize that 10⁹ is a common factor:

  (5.4×10⁹) - (3.2×10⁹) = (5.4 -3.2)×10⁹ = 2.2×10⁹

Answer: 2.2×10⁹

Step-by-step explanation:

Select the correct answer.
If `u=(1+isqrt(3))' and `v=(1+2isqrt(3)) , what is uv?
A.
*7+3isqrt(3)
B.
-5+3isqrt(3)
C.
5+2isqrt(3)
D.
*7+2isqrt(3)

Answers

Answer:

B

Step-by-step explanation:

(1+isqrt(3))(1+2isqrt(3))=1+2i√3+i√3+i√3*2i√3=3i√3-5=-5+3i√3

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