GMAT Math : Calculating the volume of a cylinder

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Example Questions

Example Question #1 : Calculating The Volume Of A Cylinder

What is the volume of a cone with a radius of 6 and a height of 7?

Possible Answers:

$\dpi{100} \small 36\pi$ $\displaystyle \dpi{100} \small 36\pi$

$\dpi{100} \small 84\pi$ $\displaystyle \dpi{100} \small 84\pi$

$\dpi{100} \small 96\pi$ $\displaystyle \dpi{100} \small 96\pi$

$\dpi{100} \small 42\pi$ $\displaystyle \dpi{100} \small 42\pi$

$\dpi{100} \small 49\pi$ $\displaystyle \dpi{100} \small 49\pi$

Correct answer:

$\dpi{100} \small 84\pi$ $\displaystyle \dpi{100} \small 84\pi$

Explanation:

The only tricky part here is remembering the formula for the volume of a cone. If you don't remember the formula for the volume of a cone, you can derive it from the volume of a cylinder. The volume of a cone is simply 1/3 the volume of the cylinder. Then,

$volume = \frac{\pi r^{2}h}{3} = \frac{\pi\cdot 6^{2}\cdot 7}{3} = 84\pi$ $\displaystyle volume = \frac{\pi r^{2}h}{3} = \frac{\pi\cdot 6^{2}\cdot 7}{3} = 84\pi$

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Example Question #2 : Calculating The Volume Of A Cylinder

What is the volume of a sphere with a radius of 9?

Possible Answers:

$\dpi{100} \small 300\pi$ $\displaystyle \dpi{100} \small 300\pi$

$\dpi{100} \small 243\pi$ $\displaystyle \dpi{100} \small 243\pi$

$\dpi{100} \small 81\pi$ $\displaystyle \dpi{100} \small 81\pi$

$\dpi{100} \small 972\pi$ $\displaystyle \dpi{100} \small 972\pi$

$\dpi{100} \small 900\pi$ $\displaystyle \dpi{100} \small 900\pi$

Correct answer:

$\dpi{100} \small 972\pi$ $\displaystyle \dpi{100} \small 972\pi$

Explanation:

$\dpi{100} \small volume = \frac{4}{3}\pi r^{3} = \frac{4}{3}\pi\times 9^{3} = 972\pi$ $\displaystyle \dpi{100} \small volume = \frac{4}{3}\pi r^{3} = \frac{4}{3}\pi\times 9^{3} = 972\pi$

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Example Question #1 : Calculating The Volume Of A Cylinder

What is the volume of a cylinder that is 12 inches high and has a radius of 6 inches?

Possible Answers:

$432\pi$ $\displaystyle 432\pi$

$464\pi$ $\displaystyle 464\pi$

$398\pi$ $\displaystyle 398\pi$

$512\pi$ $\displaystyle 512\pi$

$532\pi$ $\displaystyle 532\pi$

Correct answer:

$432\pi$ $\displaystyle 432\pi$

Explanation:

$volume=\pi r^{2}h=\pi *6^{2}*12=432\pi$ $\displaystyle volume=\pi r^{2}h=\pi *6^{2}*12=432\pi$

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Example Question #2 : Calculating The Volume Of A Cylinder

A cylindrical gas tank is 30 meters high and has a radius of 10 meters. How much oil can the tank hold?

Possible Answers:

$2800\pi$ $\displaystyle 2800\pi$

$1642\pi$ $\displaystyle 1642\pi$

$3000\pi$ $\displaystyle 3000\pi$

$300\pi$ $\displaystyle 300\pi$

$9000\pi$ $\displaystyle 9000\pi$

Correct answer:

$3000\pi$ $\displaystyle 3000\pi$

Explanation:

$V=\pi r^{2}h=\pi (10^{2})30=3000\pi$ $\displaystyle V=\pi r^{2}h=\pi (10^{2})30=3000\pi$

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Example Question #3 : Calculating The Volume Of A Cylinder

The height and the circumference of a cone are equal. The radius of the cone is 6 inches. Give the volume of the cone.

Possible Answers:

$144 \pi \textrm{ in}^{3}$ $\displaystyle 144 \pi \textrm{ in}^{3}$

$144 \pi ^{2} \textrm{ in}^{3}$ $\displaystyle 144 \pi ^{2} \textrm{ in}^{3}$

$432 \pi \textrm{ in}^{3}$ $\displaystyle 432 \pi \textrm{ in}^{3}$

$576 \pi ^{2} \textrm{ in}^{3}$ $\displaystyle 576 \pi ^{2} \textrm{ in}^{3}$

$432 \pi ^{2} \textrm{ in}^{3}$ $\displaystyle 432 \pi ^{2} \textrm{ in}^{3}$

Correct answer:

$144 \pi ^{2} \textrm{ in}^{3}$ $\displaystyle 144 \pi ^{2} \textrm{ in}^{3}$

Explanation:

The circumference of a circle with radius 6 inches is $2 \pi \cdot 6 = 12 \pi$ $\displaystyle 2 \pi \cdot 6 = 12 \pi$ inches, making this the height. The area of the circular base is $B = \pi \cdot 6^{2} = 36 \pi$ $\displaystyle B = \pi \cdot 6^{2} = 36 \pi$ square inches. The cone has volume

$V = \frac{1}{3} Bh = \frac{1}{3} \cdot 36 \pi \cdot 12 \pi = 144 \pi ^{2}$ $\displaystyle V = \frac{1}{3} Bh = \frac{1}{3} \cdot 36 \pi \cdot 12 \pi = 144 \pi ^{2}$ cubic inches.

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Example Question #1 : Calculating The Volume Of A Cylinder

The height of a cylinder is twice the circumference of its base. The radius of the base is 10 inches. What is the volume of the cylinder?

Possible Answers:

$4,000 \pi \textrm{ in}^{3}$ $\displaystyle 4,000 \pi \textrm{ in}^{3}$

$8,000 \pi \textrm{ in}^{3}$ $\displaystyle 8,000 \pi \textrm{ in}^{3}$

$4,000 \pi ^{3} \textrm{ in}^{3}$ $\displaystyle 4,000 \pi ^{3} \textrm{ in}^{3}$

$8,000 \pi ^{2} \textrm{ in}^{3}$ $\displaystyle 8,000 \pi ^{2} \textrm{ in}^{3}$

$4,000 \pi ^{2} \textrm{ in}^{3}$ $\displaystyle 4,000 \pi ^{2} \textrm{ in}^{3}$

Correct answer:

$4,000 \pi ^{2} \textrm{ in}^{3}$ $\displaystyle 4,000 \pi ^{2} \textrm{ in}^{3}$

Explanation:

The radius of the base is 10 inches, so its circumference is $2 \pi$ $\displaystyle 2 \pi$ times this, or $2 \pi \cdot 10 = 20 \pi$ $\displaystyle 2 \pi \cdot 10 = 20 \pi$ inches. The height is twice this, or $40 \pi$ $\displaystyle 40 \pi$ inches.

Substitute $r = 10 , h = 40 \pi$ $\displaystyle r = 10 , h = 40 \pi$ in the formula for the volume of the cylinder:

$V = \pi r ^{2} h$ $\displaystyle V = \pi r ^{2} h$

$V = \pi \cdot 10 ^{2}\cdot 40 \pi = 4,000 \pi ^{2}$ $\displaystyle V = \pi \cdot 10 ^{2}\cdot 40 \pi = 4,000 \pi ^{2}$ cubic inches

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Example Question #6 : Calculating The Volume Of A Cylinder

A large cylinder has a height of 5 meters and a radius of 2 meters. What is the volume of the cylinder?

Possible Answers:

$20\pi$ $\displaystyle 20\pi$ m^3 $\displaystyle m^3$

$50\pi$ $\displaystyle 50\pi$ m^3 $\displaystyle m^3$

$35\pi$ $\displaystyle 35\pi$ m^3 $\displaystyle m^3$

$15\pi$ $\displaystyle 15\pi$ m^3 $\displaystyle m^3$

$10\pi$ $\displaystyle 10\pi$ m^3 $\displaystyle m^3$

Correct answer:

$20\pi$ $\displaystyle 20\pi$ m^3 $\displaystyle m^3$

Explanation:

We are given the height and radius of the cylinder, which is all we need to calculate its volume. Using the formula for the volume of a cylinder, we plug in the given values to find our solution:

$V=\pi r^2h$ $\displaystyle V=\pi r^2h$

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

$V=20\pi$ $\displaystyle V=20\pi$ m^3 $\displaystyle m^3$

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Example Question #751 : Problem Solving Questions

Consider the Circle $\displaystyle O$:

Circle3

(Figure not drawn to scale.)

Suppose Circle $\displaystyle O$ is the base of a cylindrical silo that has a height of $30\:m$ $\displaystyle 30\:m$. What is the volume of the silo in meters cubed?

Possible Answers:

$450 \pi\:m^3$ $\displaystyle 450 \pi\:m^3$

$225 \pi\:m^3$ $\displaystyle 225 \pi\:m^3$

$6750 \pi\:m^3$ $\displaystyle 6750 \pi\:m^3$

$500 \pi\:m^3$ $\displaystyle 500 \pi\:m^3$

$900 \pi\:m^3$ $\displaystyle 900 \pi\:m^3$

Correct answer:

$6750 \pi\:m^3$ $\displaystyle 6750 \pi\:m^3$

Explanation:

To find the volume of cylinder, use the following equation:

$\small V=\pi r^2h$ $\displaystyle \small V=\pi r^2h$

In this equation, $\displaystyle r$ is the radius of the base and $\displaystyle h$ is the height of the cylinder. Plug in the given value for the height of the silo and simplify to get the answer in meters cubed:

$\small \small V=\pi (15\:m)^2*30\:m=6750 \pi\:m^3$ $\displaystyle \small \small V=\pi (15\:m)^2*30\:m=6750 \pi\:m^3$

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Example Question #8 : Calculating The Volume Of A Cylinder

A given cylinder has a radius of $\displaystyle 10$ and a height of $\displaystyle 15$. What is the volume of the cylinder?

Possible Answers:

$25\pi$ $\displaystyle 25\pi$

$150\pi$ $\displaystyle 150\pi$

$1500\pi$ $\displaystyle 1500\pi$

$60\pi$ $\displaystyle 60\pi$

$300\pi$ $\displaystyle 300\pi$

Correct answer:

$1500\pi$ $\displaystyle 1500\pi$

Explanation:

The volume $\displaystyle V$ of a cylinder with radius $\displaystyle r$ and height $\displaystyle h$ is defined as $V=\pi r^{2}h$ $\displaystyle V=\pi r^{2}h$. Plugging in our given values:

$V=\pi r^{2}h$ $\displaystyle V=\pi r^{2}h$

$V=\pi (10)^{2}(15)$ $\displaystyle V=\pi (10)^{2}(15)$

$V=\pi (100)(15)$ $\displaystyle V=\pi (100)(15)$

$V=1500\pi$ $\displaystyle V=1500\pi$

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Example Question #8 : Calculating The Volume Of A Cylinder

A cylindrical oil drum has a radius of $\displaystyle 2$ meters and a height of $\displaystyle 3$ meters. How much oil can the drum hold?

Possible Answers:

$18\pi m^{3}$ $\displaystyle 18\pi m^{3}$

$12\pi m^{3}$ $\displaystyle 12\pi m^{3}$

$10\pi m^{3}$ $\displaystyle 10\pi m^{3}$

$5\pi m^{3}$ $\displaystyle 5\pi m^{3}$

$6\pi m^{3}$ $\displaystyle 6\pi m^{3}$

Correct answer:

$12\pi m^{3}$ $\displaystyle 12\pi m^{3}$

Explanation:

Since we are looking to find out how much oil the drum can hold, we need to find the volume of the drum. The volume $\displaystyle V$ of a cylinder with radius $\displaystyle r$ and height $\displaystyle h$ is defined as $V=\pi r^{2}h$ $\displaystyle V=\pi r^{2}h$. Plugging in our given values:

$V=\pi r^{2}h$ $\displaystyle V=\pi r^{2}h$

$V=\pi (2m)^{2}(3m)$ $\displaystyle V=\pi (2m)^{2}(3m)$

$V=\pi (4m^{2})(3m)$ $\displaystyle V=\pi (4m^{2})(3m)$

$V=12\pi m^{3}$ $\displaystyle V=12\pi m^{3}$

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GMAT Math : Calculating the volume of a cylinder

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Volume Of A Cylinder

Example Question #2 : Calculating The Volume Of A Cylinder

Example Question #1 : Calculating The Volume Of A Cylinder

Example Question #2 : Calculating The Volume Of A Cylinder

Example Question #3 : Calculating The Volume Of A Cylinder

Example Question #1 : Calculating The Volume Of A Cylinder

Example Question #6 : Calculating The Volume Of A Cylinder

Example Question #751 : Problem Solving Questions

Example Question #8 : Calculating The Volume Of A Cylinder

Example Question #8 : Calculating The Volume Of A Cylinder

All GMAT Math Resources

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