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ACT Math : Solid Geometry

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Example Question #1032 : Act Math

The height of a right circular cylinder is and its radius is . What is the volume, in cubic meters, of the cylinder?

Possible Answers:

$15\pi$

$75\pi$

$45\pi$

$9\pi$

$30\pi$

Correct answer:

$45\pi$

Explanation:

The volume of a right circular cylinder is equal to its height () multiplied by the area of the circle base ( $\pi r^2$ ).

In this scenario, the Volume

$V=5* (\pi *3^2) = 45\pi$ .

Therefore, the volume is $45\pi$ .

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Example Question #751 : Geometry

What is the volume of a cylinder with a radius of four inches and a height of seven inches?

Possible Answers:

112 inches^2

$3256 \pi inches^3$

$784 \pi inches^3$

$112\pi inches^3$

$196 \pi inches^3$

Correct answer:

$112\pi inches^3$

Explanation:

Plug the radius and height into the formula for the volume of a cylinder:
$\\V = \pi *r^2*h \newline V = \pi * 4^2 * 7 \newline V = 112 \pi inches^3$

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Example Question #1034 : Act Math

What is the volume of a cylinder with a base diameter of 12 and a height of 3? Leave your answer in terms of $\pi$

Possible Answers:

108

$108\pi$

$100\pi$

$54\pi$

$36\pi$

Correct answer:

$108\pi$

Explanation:

To find the volume of a cylinder use formula:

$V = \pi r^2*h$

For a cylinder with a radius of 6 and a height of 3 this yields:

$V = \pi 6^2*3$

$=108\pi$

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Example Question #1 : How To Find The Volume Of A Cylinder

Find the volume of a cylinder whose diameter is and height is .

Possible Answers:

$288\pi$

$72\pi$

$48\pi$

$24\pi$

Correct answer:

$72\pi$

Explanation:

To find volume, simply use the following formula. Remember, you were given diameter so radius is half of that. Thus,

$V=\pi{r^2}h=\pi*3^2*8=72\pi$

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Example Question #1 : How To Find The Volume Of A Cylinder

Find the volume of cylinder with diameter of and height of .

Possible Answers:

$12\pi$

$36\pi$

$24\pi$

$18\pi$

$72\pi$

Correct answer:

$18\pi$

Explanation:

To find volume of a cylinder, simply use the following formula. Thus,

$\textup{volume}=\pi{r^2}h=\pi*(3^2)*2=\pi*9*2=18\pi$

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Example Question #1 : How To Find The Volume Of A Cylinder

Find the volume fo a cylinder whose radius is and height is .

Possible Answers:

$22\pi$

$44\pi$

$11\pi$

Correct answer:

$11\pi$

Explanation:

To solve, simply use the formula. Thus,

$V=\pi{r^2}h=\pi\cdot1^2\cdot11=\pi\cdot1\cdot11=11\pi$

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Example Question #121 : Solid Geometry

Find the volume of a cylinder with height 1 and radius 1.

Possible Answers:

$\pi$

$2\pi$

$4\pi$

$3\pi$

Correct answer:

$\pi$

Explanation:

To solve, simply use the formula for volume of a cylinder.

First, identify what is known.

Height = 1

Radius = 1

Substitute these values into the formula and solve.

Thus,

$V=\pi{r^2}h=\pi*1^2*1=\pi$

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Example Question #121 : Solid Geometry

Find the volume of a cylinder given height of and radius of .

Possible Answers:

$32\pi$

$128\pi$

$64\pi$

$16\pi$

Correct answer:

$32\pi$

Explanation:

To solve, simply use the following formula. Thus,

$V=\pi{r^2}h=\pi*2^2*8=\pi*4*8=32\pi$

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Example Question #1040 : Act Math

A cylindrical tank is used as part of a water purifying plant. When contaminated water flows into the top section of the tank, pressure forces it through a mesh filter at the bottom of the tank and clean water exits through a funnel, leaving sediment behind. The tank's filter must be replaced when the total sediment content of the tank exceeds ten percent of the tank's total volume. If the tank is 100 feet tall and 18 feet in diameter, how much sediment, in cubic feet, can the drum hold before the filter must be changed?

Possible Answers:

$760\pi$

$810\pi$

$900\pi$

$9000\pi$

$8100\pi$

Correct answer:

$810\pi$

Explanation:

The volume of a cylinder is found using the following formula:

$V = \pi r^2 h$

In this formula, the variable is the height of the cylinder and is its radius. Since the diameter is two times the radius, first solve for the radius.

$\text{Diameter}=2r$

18=2r

Divide both sides of the equation by 2.

$\frac{18}{2}=\frac{2r}{}2$

r=9

The given cylinder has a radius of 9 feet. Now, substitute the calculated and known values into the equation for the volume of a cylinder and solve.

$V=\pi\times9^{2}\times 100$

$V=8100\pi$

This is the total volume of the tank. The question asks for the volume of ten percent of the tank—the point at which the filter must be replaced. To find this, move the decimal point in the numerical measure of total volume to the left one place in order to calculate ten percent of the total volume. (Ignore $\pi$ —you can treat it like a multiplier here. Since it appears on both sides of the equals sign, it doesn't affect the decimal shift.)

$8100\pi\times 0.10=810\pi$

The tank can hold $810\pi$ cubic feet of sediment before the filter needs to be changed.

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Example Question #641 : Geometry

What is the surface area of a cylinder with a radius of 2 cm and a height of 10 cm?

Possible Answers:

40π cm²

32π cm²

36π cm²

56π cm²

48π cm²

Correct answer:

48π cm²

Explanation:

SA_cylinder = 2πrh + 2πr² = 2π(2)(10) + 2π(2)² = 40π + 8π = 48π cm²

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ACT Math : Solid Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1032 : Act Math

Example Question #751 : Geometry

Example Question #1034 : Act Math

Example Question #1 : How To Find The Volume Of A Cylinder

Example Question #1 : How To Find The Volume Of A Cylinder

Example Question #1 : How To Find The Volume Of A Cylinder

Example Question #121 : Solid Geometry

Example Question #121 : Solid Geometry

Example Question #1040 : Act Math

Example Question #641 : Geometry

All ACT Math Resources

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