GED Math - Volume of a Cylinder

Let $\pi = 3.14$

If a cylinder has a height of 7in and a radius of 4in, find the volume.

$351.68\text{in}^3$

$87.92\text{in}^3$

$175.84\text{in}^3$

$615.44\text{in}^3$

$703.36\text{in}^3$

Explanation

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

We know $\pi=3.14$ .

We know the radius of the cylinder is 4in.

We know the height of the cylinder is 7in.

Now, we can substitute. We get

$V = 3.14 \cdot (4\text{in})^2 \cdot 7\text{in}$

$V = 3.14 \cdot 16\text{in}^2 \cdot 7\text{in}$

$V = 3.14 \cdot 112\text{in}^3$

$V = 351.68\text{in}^3$

Find the volume of the cylinder if the radius is $3\pi$ and the height is $5\pi$ .

$45\pi ^4$

$9\pi ^4$

$15\pi^3$

$15\pi^2$

$90\pi ^4$

Explanation

Write the formula for a cylinder.

$V= \pi r^2h$

Substitute the dimensions.

$V= \pi (3\pi)^2(5\pi) = 45\pi ^4$

The answer is: $45\pi ^4$

While exploring the woods near your house, you find a cylindrical hole in the ground. You decide that it is dangerous and should be filled in with concrete so that nobody falls in and hurts themselves. You find that the hole is 20 feet deep and 6 feet wide. How many cubic feet of concrete will you need to fill in the hole?

Explanation

We need to find the volume of a cylinder. Use the following formula

$V=\pi r ^2 h$

A cylinder is really just a circle with height.

We know our height, 20ft.

Our radius is half of the width of the hole. In this case, our width is 6ft, so our radius is 3 ft.

Plug these in and find our volume.

$V=\pi (3ft) ^2 20ft=\pi 180ft^3=565.5ft^3$

So our answer is:

Find the volume of the cylinder with a radius of 7 and a height of 10.

$490\pi$

$70\pi$

$4900\pi$

$\frac{70}{3}\pi$

$\frac{490}{3}\pi$

Explanation

Write the formula for the volume of a cylinder.

$V= \pi r^2h$

Substitute the radius and height into the equation.

$V= \pi (7)^2(10) = \pi (49) (10) = 490\pi$

The answer is: $490\pi$

Determine the volume of a cylinder with a base area of 10, and a height of 20.

$200\pi$

$2000\pi$

Explanation

Write the formula for the volume of the cylinder.

$V = \pi r^2 h$

The base of a cylinder is a circle, and the area of the circle is $\pi r^2$ .

Substitute the base and height into the equation.

The answer is:

Barrel

The above diagram is one of a cylindrical tub. The company wants to make a cylindrical tub with three times the volume, but whose base is only twice the radius. How high should this new tub be?

$30\textrm{ in}$

$53 \frac{1}{3}\textrm{ in}$

$60\textrm{ in}$

$26 \frac{2}{3}\textrm{ in}$

Explanation

The volume of the given tub can be expressed using the following formula, setting and :

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

$V = \pi \cdot 25^{2} \cdot 40$

$V = 25,000 \pi$ cubic inches.

The new tub should have three times this volume, or

$V = 25,000 \pi \cdot 3 = 75,000 \pi$ cubic inches.

The radius is to be twice that of the above tub, which will be

$r = 25 \cdot 2 = 50$ inches.

The height can therefore be calculated as follows:

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

$\pi \cdot 50^{2} \cdot h = 75,000 \pi$

$2,500 \pi h = 75,000 \pi$

$h = \frac{75,000 \pi}{2,500 \pi} = 30$ inches

Find the volume of a cylinder with a radius of 10, and a height of 20.

$2000\pi$

$200\pi$

$\frac{200\pi}{3}$

$\frac{2000\pi}{3}$

$4000\pi$

Explanation

Write the formula for the volume of a cylinder.

$V= \pi r^2 h$

Substitute the radius and height.

$V= \pi (10)^2 (20) = \pi (100) (20)$

The answer is: $2000\pi$

Find the volume of a cylinder with a base area of 15, and a height of 10.

$150\pi$

$\frac{75}{4}\pi$

$2250\pi$

Explanation

Write the volume formula for the cylinder. The area of the base is a circle or $\pi r^2$ .

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

Substitute the base and height.

The volume is:

Find the volume of a cylinder with a radius of 5 and a height of 12.

$300 \pi$

$60\pi$

$120\pi$

$90\pi$

$400\pi$

Explanation

Write the formula for the volume of a cylinder.

$V= \pi r^2 h$

Substitute the dimensions.

$V= \pi (5)^2 (12) = \pi (25) (12 )= 300 \pi$

The answer is: $300 \pi$

One cubic foot is equal to (about) 7.5 gallons.

A circular swimming pool has diameter 60 feet and depth five feet throughout. Using the above conversion factor, how many gallons of water does it hold?

Use 3.14 for $\pi$ .

$105,975\textrm{ gal }$

$211,950\textrm{ gal }$

$7,065 \textrm{ gal }$

$24,320\textrm{ gal}$

Explanation

The pool can be seen as a cylinder with depth (or height) 5 feet, and a base with diameter 60 feet - and radius half this, or 30 feet. The capacity of the pool is the volume of this cylinder, which is

$V = \pi r ^{2} h = 3.14 \times 30^{2} \times 5 = 14,130$ cubic feet.

One cubic foot is equal to 7.5 gallons, so multiply:

$14,130 \times 7.5 = 105,975$ gallons

Volume of a Cylinder

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