GMAT Math : Calculating the volume of a cylinder

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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:

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

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

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

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

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

Correct answer:

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

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,

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

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Example Question #1 : Calculating The Volume Of A Cylinder

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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Example Question #3 : 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:

$398\pi$

$432\pi$

$464\pi$

$512\pi$

$532\pi$

Correct answer:

$432\pi$

Explanation:

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

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Example Question #1 : 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:

$3000\pi$

$9000\pi$

$1642\pi$

$300\pi$

$2800\pi$

Correct answer:

$3000\pi$

Explanation:

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

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Example Question #1 : 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:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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Example Question #6 : 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:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

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Example Question #7 : 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:

$10\pi$ m^3

$50\pi$ m^3

$15\pi$ m^3

$35\pi$ m^3

$20\pi$ m^3

Correct answer:

$20\pi$ 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:

$V=\pi r^2h$

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

$V=20\pi$ m^3

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Example Question #1 : Calculating The Volume Of A Cylinder

Consider the Circle :

Circle3

(Figure not drawn to scale.)

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

Possible Answers:

$450 \pi\:m^3$

$500 \pi\:m^3$

$225 \pi\:m^3$

$6750 \pi\:m^3$

$900 \pi\:m^3$

Correct answer:

$6750 \pi\:m^3$

Explanation:

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

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

In this equation, is the radius of the base and 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:

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

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Example Question #9 : Calculating The Volume Of A Cylinder

A given cylinder has a radius of and a height of . What is the volume of the cylinder?

Possible Answers:

$1500\pi$

$150\pi$

$60\pi$

$25\pi$

$300\pi$

Correct answer:

$1500\pi$

Explanation:

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

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

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

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

$V=1500\pi$

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Example Question #10 : Calculating The Volume Of A Cylinder

A cylindrical oil drum has a radius of meters and a height of meters. How much oil can the drum hold?

Possible Answers:

$12\pi m^{3}$

$6\pi m^{3}$

$5\pi m^{3}$

$18\pi m^{3}$

$10\pi m^{3}$

Correct answer:

$12\pi m^{3}$

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

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

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

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

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

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GMAT Math : Calculating the volume of a cylinder

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Calculating The Volume Of A Cylinder

Example Question #1 : 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 #1 : Calculating The Volume Of A Cylinder

Example Question #6 : Calculating The Volume Of A Cylinder

Example Question #7 : Calculating The Volume Of A Cylinder

Example Question #1 : Calculating The Volume Of A Cylinder

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