Question

1. a painter needs to paint the bottom of a circular pool. the pool has a radius of 30 feet. a store sells 5 - gallon cans of paint. one gallon of paint covers 300 square feet. what is the smallest number of 5 - gallon cans the painter must buy to cover the bottom of the pool? explain or show your reasoning.

Explanation:

Step1: Calculate the area of the circular pool

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 30\) feet, then \(A=\pi\times30^{2}=900\pi\approx900\times3.14 = 2826\) square feet.

Step2: Determine the number of 5 - gallon cans

Since one 5 - gallon can covers 300 square feet. Let \(n\) be the number of cans. Then \(n=\frac{2826}{300}=9.42\).

Answer:

The painter must buy 10 cans. Because we cannot buy a fraction of a can, and 9 cans (\(9\times300 = 2700\) square feet) is not enough to cover 2826 square feet, so we need to round up 9.42 to 10.