# Volumes of Shapes: Definition & Examples

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• 0:00 Definition of Volume
• 1:12 Formulas
• 2:06 Examples
• 3:26 Lesson Summary

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Lesson Transcript
Instructor: Jennifer Beddoe
Volume is defined as the 3-dimensional space enclosed by a boundary. In this lesson we will define volume, give some of the most common formulas and then work some example problems to become familiar with the formulas. There will be a quiz at the end of the lesson for practice.

## Definition of Volume

Volume is defined as the amount of space taken up by an object. It is most often described in terms of meters cubed (m^3). One way to find the volume of an object is to completely submerge the object in water and measure the volume of water that is displaced by the object. The amount of water displaced is equal to the volume of the object. If you don't happen to have a large amount of water handy, or the object you are interested in would not fare well in water, there are formulas you can use instead. Determining the volume of cubes or rectangular prisms can be found quite easily. You can also determine the volume of more complex shapes such as cones, pyramids, cylinders or spheres.

Determining the volume of an object can be of practical importance. Knowing the volume of an object can help you determine how much would be needed to fill that object, like the amount of water needed to fill an aquarium. Knowing how to determine volume can also help you win some money. How? Well, if you can determine the volume of a container and the volume of a jelly bean, you can win the 'Guess How many Jelly Beans are in this Jar?' contest.

## Formulas

The basic geometric shapes for which there are volume formulas are the cube, rectangular prism, cylinder, cone, pyramid and sphere. The formulas for each of these shapes are:

Cube volume (V) is equal to s^3 where s is the side of the cube, V=s^3.

Rectangular Prism volume (V) is equal to L times W time H, where L is the length, W is the width and H is the height, V = L x W x H.

Cylinder volume (V) is equal to (pi)r^2 times h, where r is the radius and h is the height, V = (pi)r^2 x h.

Sphere volume (V) is equal to 4/3(pi)r^3, where r is the radius, V = 4/3(pi)r^3.

Pyramid volume (V) is equal to 1/3Ah, where A is the area of the base and h is the height, V = 1/3Ah.

Cone volume (V) is 1/3(pi)r^2h, where r is the radius and h is the height, V = 1/3(pi)^2h.

## Examples

Let's look at some examples:

1. A swimming pool is 8 meters wide, 25 meters long and 1.5 meters deep. What is the volume of water in the pool?

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