Question

At the park there is a pool shaped like a circle with radius 10 yd. A ring-shaped path goes around the pool. Its width is 5 yd.We are going to give a new layer of coating to the path. If one gallon of coating can cover 7y * d ^ 2 how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for pi.

Answer 1

Step 1:

Concept

`Area\text{ of the colored path = Area of inner circle - Area of outer circle}`

Step 2:

`\begin{gathered} Inner\text{ radius r = 10 yd} \\ Outer\text{ radius R = 15 yd} \\ \pi\text{ = 3.14} \end{gathered}`

Step 3:

Substitute in the formula to find the area of the colored part.

`\begin{gathered} Area\text{ of the colored part = 3.14}*15^2\text{ - 3.14}*10^2 \\ =\text{ 706.5 - 314} \\ =\text{ 392.5 yd}^2 \end{gathered}`
`\begin{gathered} Number\text{ of gallons of coating needed =}(392.5)/(7) \\ =\text{ 56.071428571 gallons} \end{gathered}`

Final answer

57 gallons