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ACT Math : Geometry

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Example Questions

Example Question #2 : Cylinders

The radius of a cylinder is five and its height is nine. What is its volume?

Possible Answers:

$25\pi+9$

$2025\pi$

$45\pi$

$405\pi$

$225\pi$

Correct answer:

$225\pi$

Explanation:

To solve this question, you must remember that the formula for volume is the product of the area of the base and the height. The area of the base of this cylinder is $\pi r^2$ .

$V=A_b*h=\pi r^2h$

Plug in the given radius and height to solve.

$V=\pi(5)^2(9)$

$V=\pi(25)(9)$

$V=225\pi$

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Example Question #3 : Cylinders

What is the volume of a round metal washer with an outer radius of 8 in, an inner radius of 2 in, and a thickness of 0.5 in?

Possible Answers:

$16\pi\ in^3$

$30\pi\ in^3$

$24\pi\ in^3$

$6\pi\ in^3$

$10\pi\ in^3$

Correct answer:

$30\pi\ in^3$

Explanation:

The volume of a cylinder is given by the formula: $V=\pi r^2h$ .

For a shape with a hole through the center, the final volume is equal to the total volume of the shape minus the volume of the inner hole. In this question, we are looking for the volume given by the larger radius minus the volume given by the smaller radius. The height is equal to the thickness of the washer.

$V=\pi r_1^2h-\pi r_2^2h$

$V=\pi(8)^2(0.5)-\pi(2)^2(0.5)$

$V=\pi(64)(0.5)-\pi(4)(0.5)$

$V=32\pi-2\pi$

$V=30\pi\ in^3$

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Example Question #4 : How To Find The Volume Of A Cylinder

How much more volume can a cylinder hold than a cone given that both have the same radius and height?

Here B represents the area of the Base, and h the height.

Possible Answers:

$\frac{2}{3}Bh$

$\frac{1}{4}Bh$

$\frac{1}{2}Bh$

$\frac{1}{3}Bh$

None of the answers are correct

Correct answer:

$\frac{2}{3}Bh$

Explanation:

Cylinder: V=Bh Cone: $V=\frac{1}{3}Bh$

Thus the difference is 2/3Bh and that means a cylinder can hold 2/3Bh more given the same radius and height.

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

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

Possible Answers:

$45\pi$

$30\pi$

$75\pi$

$15\pi$

$9\pi$

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 #5 : How To Find The Volume Of A Cylinder

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

Possible Answers:

112 inches^2

$112\pi inches^3$

$3256 \pi inches^3$

$196 \pi inches^3$

$784 \pi inches^3$

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 #7 : Cylinders

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:

$36\pi$

$100\pi$

$54\pi$

108

$108\pi$

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 #2 : How To Find The Volume Of A Cylinder

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

Possible Answers:

$288\pi$

$24\pi$

$72\pi$

$48\pi$

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 #3 : How To Find The Volume Of A Cylinder

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

Possible Answers:

$36\pi$

$18\pi$

$24\pi$

$12\pi$

$72\pi$

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 #5 : How To Find The Volume Of A Cylinder

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

Possible Answers:

$44\pi$

$22\pi$

$11\pi$

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 #11 : Cylinders

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

Possible Answers:

$2\pi$

$4\pi$

$\pi$

$3\pi$

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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ACT Math : Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #2 : Cylinders

Example Question #3 : Cylinders

Example Question #4 : How To Find The Volume Of A Cylinder

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

Example Question #5 : How To Find The Volume Of A Cylinder

Example Question #7 : Cylinders

Example Question #2 : How To Find The Volume Of A Cylinder

Example Question #3 : How To Find The Volume Of A Cylinder

Example Question #5 : How To Find The Volume Of A Cylinder

Example Question #11 : Cylinders

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