Question

Consider the rectangular box with square bottom as shown below. All dimensions are measured in inches.

Use lower case letter w for the width of the box and lower case letter h for the height of the box.
(a) If the height of the box is nine inches greater than the width of the box, express height in terms of width.

(b) Express the volume of the box in terms of height only. No need to distribute your answer.

Answer 1

Explanation:

Dimensions of the box, considering the base is a square:

• Length = w
• Width = w
• Height = h

(a)

The height is 9 inches greater than the width:

• h = w + 9

(b)

Express the width in terms of height:

• w = h - 9

Volume of the box:

• V = base * height
• V = w²h
• V = (h - 9)²h