Question

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

Answer 1

The volume of the dresser can be calculated through the formula:

$V=A_b\ast h$

where Ab is the area of the base and h the height of the building, then, clear the equation for the area of the base,

$A_b=\frac{V}{h}$

Now replace with the given values,

$\begin{gathered} A_b=\frac{42ft^3}{3ft} \\ A_b=14ft^2 \end{gathered}$

Then, suppose the base is a rectangle, then the area's formula is:

$A_b=l\ast w$

give the length a value of 2 ft, and clear the formula for the missing measurement

$\begin{gathered} 14ft^2=2ft\ast w \\ w=\frac{14ft^2}{2ft} \\ w=7ft \end{gathered}$

Answer:

a. 14 ft²

b. length=2ft; width=7ft

c.