# Volume of a Rectangular Prism

Companies need to know the volume of a box in order to determine how much of their product will fit inside.

Here is an example:

The volume is equal to the number of 1 in x 1 in x 1 in cubes we can fit inside this box.

There could be 15 cubes across the length by 4 across the width, making a bottom layer of 15 x 4 = 60 cubes. You can also think of this as the area of the base.

Notice that the height of the box is 8 in. That means that we could fit 8 layers of 60 cubes.

In other words, the volume of this box is 480 cubic inches.

This could be simplified to the formulas

**V = Bh**or

**V = l w h**for all rectangular prisms.

Let's Practice! Determine the volume of each prism.

1.)

V = l w h

3.)

4.)

V = Bh

V = (112 in.

V = 2576 in.

V = l w h

V = (25 in.)(3 in.)(7 in.)

V = (75 in

V = 525 in

2.)
V = (75 in

^{2})(7 in)V = 525 in

^{3} V = l w h

V = (4.5 cm)(3.2 cm)(4.2 cm)

V = 60.48 cm

V = (4.5 cm)(3.2 cm)(4.2 cm)

V = 60.48 cm

^{3}3.)

4.)

V = Bh

V = (112 in.

^{2})(23 in.)

V = 2576 in.

^{3}

**Let's Review**

The volume of a prism is the space that fills it. You can determine the volume of a rectangular prism by either multiplying the area of the base times the height or by multiplying the length, width and height.

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