Question

You are constructing a concrete landing pad for a helicopter. You have 4704 cubic feet of concrete.

Answer 1

a) We have to calculate the height of the pad.

We know that the volume will be 4704 cubic feet.

We also know that the base of the pad is a square of side length 56 feet.

As the volume is the area of the base times the height, we can find the height by dividing the volume by the base area:

$\begin{gathered} V=A_b\cdot h \\ h=\frac{V}{A_b}=\frac{4704\text{ ft}^3}{(56\text{ ft})^2}=\frac{4704}{3136}\text{ ft}=1.5\text{ ft} \end{gathered}$

The height is 1.5 feet.

b) Now, we have a circular pad of which we know the height (1.5 feet) and the volume (4705 ft³). The area of the base will have to be the same as the are of the square: 3136 ft².

The area of this circular pad can be expressed as πD²/4, so we can calculate the diameter D as:

$\begin{gathered} A=3136 \\ \frac{\pi D^2}{4} \\ D^2=3136*\frac{4}{\pi} \\ D^2=3136*\frac{4}{3.14} \\ D^2=3994.9045 \\ D=\sqrt{3994.9045} \\ D\approx63.21 \end{gathered}$

The diameter is approximately 63.21 feet.

Answer:

a) The pad will be 1.5 feet thick

b) The diameter will be 63.21 feet.