Question

at the park there is a pool shaped like a circle. a ring - shaped path goes around the pool. its inner diameter is 24 yd and its outer diameter is 34 yd. we are going to give a new layer of coating to the path. if one gallon of coating can cover 8 yd², 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 π.)

Explanation:

Step1: Calculate the area of the outer circle

The formula for the area of a circle is \(A = \pi r^{2}\). The radius of the outer circle \(R=\frac{34}{2}=17\) yd. So the area of the outer circle \(A_{1}=3.14\times17^{2}=3.14\times289 = 907.46\) \(yd^{2}\)

Step2: Calculate the area of the inner circle

The radius of the inner circle \(r = \frac{24}{2}=12\) yd. So the area of the inner circle \(A_{2}=3.14\times12^{2}=3.14\times144=452.16\) \(yd^{2}\)

Step3: Calculate the area of the ring - shaped path

The area of the ring - shaped path \(A=A_{1}-A_{2}\). Substitute the values of \(A_{1}\) and \(A_{2}\): \(A = 907.46-452.16=455.3\) \(yd^{2}\)

Step4: Calculate the number of gallons of coating

Since one gallon of coating can cover \(8\) \(yd^{2}\), the number of gallons \(n=\frac{A}{8}\). Substitute \(A = 455.3\): \(n=\frac{455.3}{8}=56.9125\)

Since the number of gallons must be a whole number, we need to round up.

Answer:

\(57\)