GMAT Quantitative - Calculating the volume of a cylinder

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

$32\pi$

$16\pi$

$\24\pi$

$8\pi$

Explanation

To find the volume of a cylinder, you must use the following equation:

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

Thus,

$V=\pi(2^2)(8)=32\pi$

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

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

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

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

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

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

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.

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?

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

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

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

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

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

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

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

$81\pi$

$27\pi$

$64\pi$

$9\pi$

Explanation

To find the volume, you must use the following formula.

$V=\pi{r^2}h=\pi(3^2)(9)=81\pi$

A right circular cylinder has bases of radius $\pi ^{x}$ ; its height is $\pi ^{y}$ . Give its volume.

$\pi^{2 x+y+1}$

$\pi^{ x+2y+1}$

$\pi^{ x+y+1}$

$\pi ^{ 2y+1 } + \pi ^{x+y+1}$

$\pi ^{ 2x+1 } + \pi ^{x+y+1}$

Explanation

The volume of a cylinder can be calculated from its radius and height as follows:

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

Setting $r = \pi^{x}$ and $h = \pi ^{x}$ :

$V = \pi \cdot (\pi^{x}) ^{2} \cdot \pi^{y}$

$V = \pi^{1} \cdot \pi^{2 x} \cdot \pi^{y}$

$V = \pi^{1+2 x+y}$ or $V = \pi^{2 x+y+1}$

The height of a cylinder is $\pi ^{x}$ ; its bases are circles with radius $\pi$ .

Give the volume of the cylinder.

$\pi ^{x+3}$

$\pi ^{x+2}$

$\pi ^{2x+2}$

$\pi ^{2x+1}$

$\pi ^{2x+3}$

Explanation

The volume of a cylinder can be calculated from its radius and height as follows:

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

Setting $h = \pi ^{x}$ and $r = \pi$ .

$V = \pi \cdot \pi ^{2} \cdot \pi ^{x} = \pi^{1} \cdot \pi ^{2} \cdot \pi ^{x} = \pi ^{1+2+x} = \pi ^{x+3}$

Consider the Circle :

Circle3

(Figure not drawn to scale.)

Suppose Circle is the base of a cylindrical silo that has a height of . What is the volume of the silo in meters cubed?

$6750 \pi:m^3$

$450 \pi:m^3$

$225 \pi:m^3$

$900 \pi:m^3$

$500 \pi:m^3$

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:

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

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

$20\pi$

$10\pi$

$50\pi$

$35\pi$

$15\pi$

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:

$V=\pi r^2h$