Question

at the park there is a pool shaped like a circle with diameter 24 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 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.)
□ gallons of coating

Explanation:

Step1: Find the radius of the inner circle

The diameter of the inner circle (pool) is 24 yd, so the radius \( r_{inner} = \frac{24}{2} = 12 \) yd.

Step2: Find the radius of the outer circle

The width of the path is 5 yd, so the radius of the outer circle \( r_{outer} = 12 + 5 = 17 \) yd.

Step3: Calculate the area of the path (annulus)

The area of an annulus is \( A = \pi (r_{outer}^2 - r_{inner}^2) \). Substituting the values, we get \( A = 3.14 \times (17^2 - 12^2) \). First, calculate \( 17^2 = 289 \) and \( 12^2 = 144 \). Then, \( 289 - 144 = 145 \). So, \( A = 3.14 \times 145 = 455.3 \) square yards.

Step4: Calculate the number of gallons needed

One gallon covers 8 square yards, so the number of gallons \( n = \frac{455.3}{8} \approx 56.9125 \). Since we need a whole number of gallons, we round up to the next whole number, so \( n = 57 \).

Answer:

57