Question

The width of a plastic storage box is 2 ft longer then the height the length is a 5 ft longer than the height the volume is 216ft3

What is the formula for the volume of a rectangular prism?

What variable expressions represent the length height and width?

What equation represents the volume of the plastic storage box

Answer 1

• See below

Explanation:

Let the dimensions are width - w, length - l and height - h.

Given

• w = h + 2,
• l = h + 5,
• Volume = 216 ft³.

Solution

Formula for volume:

• V = lwh

Variable expressions for length, height and width:

• l = h + 5,
• h,
• w = h + 2

Equation for the volume of this box:

• V = lwh

Substitute the variables:

• V = h(h + 2)(h + 5)

or

• h(h + 2)(h + 5) = 216

Answer 2

• a) V = l × w × h
• b) l = (h + 5), w = (h + 2), h = h
• c) 216 = (h + 5)(h + 2)(h)

Explanation:

a) Formula we use,

→ V = l × w × h

b) The variable expressions are,

→ l = (h + 5)

→ w = (h + 2)

→ h = h

c) Forming required equation,

→ V = l × w × h

→ V = (h + 5)(h + 2)(h)

→ 216 = (h + 5)(h + 2)(h)

These are the required answers.