A painter needs to paint the bottom of a circular pool. The pool has a diameter of 60 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.
First, let's calculate the area of the bottom of the circular pool:
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
The diameter of the pool is 60 feet, so the radius (r) would be half of that, so r = 60 feet / 2 = 30 feet.
Now, calculating the area:
A = πr^2
A = π * (30 feet)^2
A = π * 900 square feet
A = 2827.43 square feet (approximately, using π ≈ 3.14159)
So, the bottom of the pool has an area of about 2827.43 square feet.
Next, let's figure out how much paint is needed to cover that area:
1 gallon of paint covers 300 square feet.
To find out how many gallons are needed to cover 2827.43 square feet, divide the total area by the coverage of 1 gallon of paint:
Number of gallons required = Total area / Coverage per gallon
Number of gallons required = 2827.43 square feet / 300 square feet per gallon
Number of gallons required = 9.42 gallons (approximately)
Since paint can only be bought in 5-gallon cans and you can't purchase a fraction of a can, the painter will need to buy whole cans.
Let's divide the number of gallons needed by the size of the can:
Number of 5-gallon cans required = Number of gallons required / 5
Number of 5-gallon cans required = 9.42 / 5
Number of 5-gallon cans required = 1.884
The painter cannot buy a fractional part of a can and needs to have enough paint to cover the entire area, so the painter must round up to the next whole number:
So, the painter must buy 2 cans of 5-gallon paint to have enough to cover the whole pool. These 2 cans will provide the painter with a total of 10 gallons of paint, which is slightly more than the 9.42 gallons calculated as necessary to cover the pool.