Calculating the volume of a cylinder - GMAT Quantitative

Card 1 of 128

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

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

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

Question

Consider the Circle :

(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?

Tap to reveal answer

Answer

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:

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

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

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

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

$V=1500\pi$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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:

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

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

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

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

← Didn't Know|Knew It →

Question

Daisy has an empty cylindrical water bottle that has a radius of and a height of . How much water can she add to the bottle to fill it up?

Tap to reveal answer

Answer

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

$V=\pi (3cm)^{2}(15cm)$

$V=\pi (9cm^{2})(15cm)$

$V=135\pi cm^{3}$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

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

Thus,

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

To solve, you must use the following equation:

$V=\pi{r^2}h$ , given and . Thus,

$V=\pi(2^2)(6)=24\pi$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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:

$V=\pi r^2h$

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

$V=20\pi$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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,

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

Question

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

Give the volume of the cylinder.

Tap to reveal answer

Answer

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 $r = \pi$ .

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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,

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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

← Didn't Know|Knew It →

0

Knew It