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## Key Concepts

### Introduction

#### Volume

Volume is the number of cubic units contained in a solid. It is measured in cubic units.

The basic formula is V = Bh, where B = area of the base, h = height.

#### Find the number of unit cubes

Example 1:

Find the volume of the puzzle piece shown in cubic units.

Solution:

To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows:

The base is 3 units by 1 unit. So, it contains 3 × 1, or 3 unit cubes.

The top layer is 3 units by 1 unit. So, it contains 3 × 1, or 3 unit cubes.

The upper left box is 1 unit by 1 unit1. So, it contains 1 × 1, or 1 unit cube.

By the Volume Addition Postulate, the total volume of the puzzle piece is 3 + 3 + 1 = 7 cubic units.

Example 2:

Find the volume of the solid in cubic units.

Solution:

To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows:

Front Layer:

Middle Layer:

Back Layer:

By the Volume Addition Postulate, the total volume of the solid is 11 + 11 + 11 =33 cubic units.

### Find volumes of prisms and cylinders

#### Volume of a prism

The volume of a right rectangular prism is equal to the product of the height and the area of the base.

V = Bh

Where B is the area of the base and h is the height.

#### Volume of a Cylinder

The volume of a cylinder is equal to the product of the height and the area of the base.

V = Bh = πr2

Where B is the area of the base, h is the height, and r is the radius of the base.

Example 3:

Find the volume of the following triangular prism.

Solution:

The area of a base is ½ (10)(8) = 40 and l = 3.

V = Area of a base x l

V = 40(3) = 120 cubic units

Example 4:

A soda can measures 5.5 inches high, and its diameter is 2.5 inches. Find the  approximate volume.

Solution:

The diameter is 2.5 in. The radius is 2.5 ÷ 2 inches.

V = pr2

V = p(1.252)(5.5)

V » 26.98 in3

## Exercise

1. Explain in your own words how to find the volume of a figure. Give an example.
2. Find the volume of the given cube
1. Find the volume of the figure.
1. Find the volume of the figure.
1. Find the volume of the figure.
1. Find the volume of the figure.
1. Find the volume of the figure.
1. A birthday cake has three layers. The top cake has a diameter of 8 inches and is 3 inches deep. The middle cake is 12 inches in diameter and is 4 inches deep. The bottom cake is 14 inches in diameter and is 6 inches deep. Find the volume of the entire cake, ignoring the icing.
1. Find the volume of a square prism that has a base edge length of 5 feet and a height of 12 feet.
1. Find the volume of the solid prism shown below.

### What have we learned

• Find the number of unit cubes in the given solid shape.
• Find volume of a prism by using the formula.
• Find volume of a cylinder by using the formula.

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