Solid geometry is concerned with three-dimensional shapes.

In these lessons, we will learn:

In these lessons, we will learn:

- how to find the volume of cylinders
- how to find the volume of hollow cylinders or tubes or pipes
- how to solve word problems about cylinders.

A cylinder is a solid with two congruent circles joined by a curved surface.

In the above figure, the radius of the circular base is *r *and the height is *h*.

The volume of the cylinder is the area of the base × height. Since the base is a circle and the area of a circle is π*r*^{2} then the volume of the cylinder is π*r*^{2} × *h.*

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Surface Area of cylinder = 2π*r*^{2}* *+ 2π*rh*

* Example: *

Calculate the volume of a cylinder where:

a) the area of the base is 30 cm ^{2} and the height is 6 cm.

b) the radius of the base is 14 cm and the height is 10 cm.

* Solution:*

a)

b)

Examples:

1. Find the volume of cylinder with radius of 5.5 feet and a height of 11.4 feet.

2. Find the volume of cylinder with diameter of 12 inches and a height of 29 inches.

Example:

Find the volume with r = 9 in and h = 12 in. (Leave your answer in &oi; form)

Sometimes you may be required to calculate the volume of a hollow cylinder or tube or pipe.

Volume of hollow cylinder:

= π*R*^{2}* h* – π*r*^{2}* h
*= π

* Example: *

The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the volume of the metal used.

* Solution:
*The cross section of the pipe is a ring:

Area of ring = [ π (2.4)

Volume of pipe = 1.76 π × 10 = 55.3 cm^{3}

Volume of metal used = 55.3 cm^{3}

**How to calculate the volume of the shaded area of a cylinder?**
The shape forms a tube or pipe.

These videos show how to solve word problems about cylinders.

Examples:1. A cylindrical can is packed in a box. What is the volume of empty space between the can and the box?

2. Emma has two prism-shaped containers. One has a volume of 9 1/3 cubic feet. How many smaller prisms would it take to fill the larger prism?

Examples:

A cylindrical can is packed securely in a box.

a) Find the radius and height of the can.

b) What is the volume of the empty space between the can and the box?

c) Find the ratio of the volume of the can to the volume of the box.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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