Question

A layer of crushed rock must be spread over a circular area 20 feet in diameter. How deep a layer will be obtained using 150 ft.³ of rock? Round to the nearest hundredth as needed.

Answer 1

The Solution:

Given that a layer of a crushed rock must be spread over a circular area of 20 feet in diameter, means that the radius of the circular area is 20 divided by 2, which gives 10 feet as radius.

$\begin{gathered} r=\frac{D}{2} \\ \text{ Where D=diameter=20} \\ r=\text{ radius=?} \\ r=\frac{20}{2}=10\text{ ft} \end{gathered}$

We are required to find the height of a layer that gives 150 cubic feet of the rock.

This means that the layer of the rock must be cylindrical. So, by formula, the volume of a cylindrical figure is given below:

$V=\pi r^2h=150ft^3$

In this case,

$\begin{gathered} r=\text{ radius=10 ft} \\ h=\text{ height=?} \end{gathered}$

Substituting in the formula above, we get

$\pi(10)^2h=150$

Simplifying to get the value of h, we have

$\begin{gathered} \frac{100\pi h}{100\pi}=\frac{150}{100\pi} \\ \\ h=0.4775\approx0.48\text{ ft} \end{gathered}$

Therefore, the correct answer is 0.