Right Prism: Volume

How to find the volume of a right prism: formula, 3 examples, and their solutions.

Formula

Formula

V = Bh

V: Volume of a right prism
B: Base area
h: Height

Example 1

Example

Solution

Find the base area B.

The base is a rectangle.
Its sides are 7 and 5.

So the area of the rectangle is
B = 7⋅5.

7⋅5 = 35

So the base area B is 35.

The height h is 8.

B = 35
h = 8

Then the volume V
is equal to,
the base area, 35
times,
the height h, 8.

35⋅8 = 280

So the volume of the right prism is 280.

Example 2

Example

Solution

Find the base area B.

The base is an equilateral triangle.
Its side is 4.

So the area of the equilateral triangle is
B = [√3/4]⋅42.

[√3/4]⋅42
= √3⋅4
= 4√3

So the base area B is 4√3.

The height h is 7.

B = 4√3
h = 7

Then the volume V
is equal to,
the base area, 4√3
times,
the height h, 7.

4√3⋅7 = 28√3

So the volume of the right prism is
28√3.

Example 3

Example

Solution

By using the given net,
draw the 3D figure of the box.

It's a right prism.

Find the base area B.

The base is a rectangle.
Its sides are 11 and 5.

So the area of the rectangle is
B = 11⋅5.

11⋅5 = 55

So the base area B is 55.

The height h is 3.

B = 55
h = 3

Then the volume V
is equal to,
the base area, 55
times,
the height h, 3.

55⋅3 = 165

So the volume of the right prism is 165.