Question

at the park there is a pool shaped like a circle. a ring - shaped path goes around the pool. its inner diameter is 16 yd and its outer diameter is 24 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. (use the value 3.14 for π.)

Explanation:

Step1: Find radii of inner and outer circles

Inner diameter = 16 yd, so inner radius \( r = \frac{16}{2} = 8 \) yd.
Outer diameter = 24 yd, so outer radius \( R = \frac{24}{2} = 12 \) yd.

Step2: Calculate area of the ring (annulus)

Area of annulus = \( \pi(R^2 - r^2) \)
Substitute \( R = 12 \), \( r = 8 \), \( \pi = 3.14 \):
\( 3.14\times(12^2 - 8^2) = 3.14\times(144 - 64) = 3.14\times80 = 251.2 \) yd².

Step3: Find number of gallons needed

1 gallon covers 5 yd², so gallons = \( \frac{251.2}{5} = 50.24 \).
Since gallons must be whole number, round up to 51 (as 50 gallons would cover \( 50\times5 = 250 \) yd², less than 251.2).

Answer:

51