Question

hello I'm stuck on this homework problem and need help thank you

Answer 1

Given:

Inner radius circle = 10yd

Outer radius circle = 14 yd

One gallon of coating can cover = 4

Find-: How many gallons of coating do we need?

Sol:

The area of a circle is:

$A=\pi r^2$

The area of the outer circle is:

$\begin{gathered} A=\pi r^2 \\ \\ =\pi(14)^2 \\ \\ =196\pi \end{gathered}$

The area of the inner circle:

$\begin{gathered} A=\pi r^2 \\ \\ A=\pi(10)^2 \\ \\ A=100\pi \end{gathered}$

So the pool area is:

$\begin{gathered} \text{ Area of pool = Area of outer circle - area of inner circle} \\ \\ =196\pi-100\pi \\ \\ =96\pi \end{gathered}$

If one gallon of coating covers 4.

$\begin{gathered} =\frac{96\pi}{4} \\ \\ =24\pi \\ \\ =75.4 \end{gathered}$

So 75 gallons use for coating.