Volume of Prisms and Cylinders

Volume of Prisms and Cylinders

Definition

Volume - the amount of space that an object occupies/contains

How to find the Volume of a Prism

Volume is equal to the "area of the Base" times "height"

V = Bh

B -> Area of the base shape

-> different from lowercase b

Example 1

The area of the hexagonal base of this prism is 23 in². The height of the prism is 7 in. What is the volume of the prism?

V = Bh

V = (23) * (7)

V = 161 in³

Multiple Choice

In the diagram, the area of the pentagonal base is 43 mm². Find the volume of the pentagonal prism.

• 129 mm³

• 345 mm³

• 645 mm³

• 27,735mm³

Common Area Equations

Triangle:  $\frac{bh}{2}$  

Rectangle:  $lw$  or  $bh$  

Circle:  $\pi r^2$  

Multiply these equations with the height/length of the prism to get the volume.

Example 2

A triangular prism has a length of 10 cm. The height of triangle is 6cm. The base of the base triangle is 4 cm. What is the volume?
height (prism) = 10, base = 4, height (triangle) = 6

 $V\ =\ Bh\ =\ \frac{bh}{2}\cdot h$ 

 $V=\frac{4\cdot6}{2}\cdot10=\frac{24}{2}\cdot10=12\cdot10=120$  

Multiple Choice

Find the volume of the figure. Round to the nearest tenth.

• 80 cm³

• 40 cm²

• 80 cm²

• 40 cm³

Example 3

A cylinder has a height of 15 ft. The diameter of the cylinder is 10 ft. What is the volume?

 $V=Bh$               $A=\pi r^2$  

 $V=\pi r^2h$  

 $V=\pi\left(5\right)^2\left(15\right)$  

 $V=1178.1\ ft^3$  

Multiple Choice

Find the volume of the cylinder.

• 282.6
• 516.2
• 133
• 214