Exercise 1 Page p30

We can calculate the volume of a rectangular prism by multiplying its length, width, and height.

V = ℓ \cdot w \cdot h

We have been told that the dimensions of our prism are

ℓ = 5,

w = 3,

and

h = 2

centimeters.

Using these values and the formula, let's calculate the volume!

V = ℓ \cdot w \cdot h

SubstituteValues

Substitute values

V = 5 \cdot 3 \cdot 2

Multiply

V = 30

The volume of the rectangular prism is

30

cubic centimeters.

Extra

Formula for the Volume

We know that the volume is the measure of space occupied by a solid. We can calculate the volume of a solids by using the area of one parallel polygon and the height of the solids. This can be written as the following formula.

V = B h

Here,

B

is the base area of the parallel polygon, and

h

is the height of the solid. This formula is more general than the one in the solution, and is valid for all types of solids. Different solids may have different formulas to calculate their volume, all of them are based in the above formula. Let's see some examples!3

Name	$V = B h$
Cube	$V = (s^{2}) s = s^{3}$
Cone	$V = \frac{1}{3} π r^{2} h$
Cylinder	$V = π r^{2} h$
Sphere	$V = \frac{4}{3} π r^{3}$

For those of you who are interested in learning more about volume, you can read more about them on the following pages.

Cavalieri's Principle
Volumes of Similar Solids
Volume of a Pyramid