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=(D)/(2) \\ \text{ Where D=diameter=20} \\ r=\text{ radius=?} \\ r=(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} (100\pi h)/(100\pi)=(150)/(100\pi) \\ \\ h=0.4775\approx0.48\text{ ft} \end{gathered}`

Therefore, the correct answer is 0.