Question

at the park there is a pool shaped like a circle. a ring - shaped path goes around the pool. its inner radius is 10 yd and its outer radius is 13 yd.
we are going to give a new layer of coating to the path. if one gallon of coating can cover 5 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. if necessary, refer to the list of geometry formulas.
gallons of coating

Explanation:

Step1: Calculate the area of the outer circle

The formula for the area of a circle is \(A = \pi r^{2}\). For the outer circle with radius \(r_{outer}=13\) yd, \(A_{outer}=\pi\times(13)^{2}= 169\pi\) \(yd^{2}\).

Step2: Calculate the area of the inner circle

For the inner circle with radius \(r_{inner} = 10\) yd, \(A_{inner}=\pi\times(10)^{2}=100\pi\) \(yd^{2}\).

Step3: Calculate the area of the ring - shaped path

The area of the ring - shaped path \(A = A_{outer}-A_{inner}\). Substitute the values: \(A=(169\pi - 100\pi)=69\pi\) \(yd^{2}\). Using \(\pi\approx3.14\), \(A = 69\times3.14=216.66\) \(yd^{2}\).

Step4: Calculate the number of gallons of coating

If one gallon of coating covers \(5\) \(yd^{2}\), then the number of gallons \(n=\frac{A}{5}\). Substitute \(A = 216.66\): \(n=\frac{216.66}{5}=43.332\). Since the number of gallons must be a whole number and we can't have a fraction of a gallon (we need to cover the entire area), we use the ceiling function. So \(n = 44\).

Answer:

44