Question

You are building a 3-foottall dresser. You want the volume to be 42 cubic feet.a. What should the area of the base be?b. Give a possible length & width of the base.c. Make a hand drawn sketch of the dresser with the dimensions you chose.

Answer 1

a. 14 ft²

b. length = 7 ft, width = 2 ft

c.

Explanation

a. The dresser has a shape of a rectangular prism. Then, the volume of the dresser is calculated as follows:

`V=\text{ Area of the base}\cdot\text{ height}`

Substituting with V = 42 cubic ft, and height = 3 ft, and solving for the area of the base:

`\begin{gathered} 42=\text{ Area of the base }\cdot3 \\ (42)/(3)=\text{ Area of the base} \\ 14\text{ ft}^2\text{ = Area of the base} \end{gathered}`

b. The base of the dresser is a rectangle. Then, the area of the base is calculated as follows:

`A=\text{ length}\cdot\text{ width}`

Assuming the length is 7 ft, and substituting A = 14 sq ft, the width must be:

`\begin{gathered} 14=7\cdot\text{ width} \\ (14)/(7)=\text{ width} \\ 2\text{ ft = width} \end{gathered}`