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? and the correct answer is 2 how did I get 2?
To determine how many 5-gallon cans of paint the painter needs to buy, let's calculate the area of the circular pool bottom and then figure out how much paint will be necessary to cover that area.
First, we calculate the area of the pool:
The diameter of the pool is 60 feet, so the radius (r) is half of that, which is 30 feet.
The area (A) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the given radius:
\[ A = \pi (30)^2 \]
\[ A = \pi (900) \]
\[ A = 2827.4333882308138 \text{ square feet} \] (approximately, since \(\pi\) is irrational)
This is the area that needs to be covered by paint.
Next, we use the coverage rate for the paint:
One gallon of paint covers 300 square feet.
Let's determine the total gallons of paint needed:
\[ \text{Total gallons} = \frac{\text{Area of the pool}}{\text{Coverage per gallon}} \]
\[ \text{Total gallons} = \frac{2827.4333882308138}{300} \]
\[ \text{Total gallons} = 9.424777960769379 \] (approximately)
Since paint can only be bought in whole 5-gallon cans, we need to round up to the nearest whole can. So the painter needs at least 10 gallons of paint to cover the pool bottom. Dividing the total required gallons by the size of each can:
\[ \text{Total 5-gallon cans needed} = \frac{10 \text{ gallons}}{5 \text{ gallons per can}} \]
\[ \text{Total 5-gallon cans needed} = 2 \text{ cans} \]
Therefore, the painter must buy a minimum of 2 cans of paint to have the 10 gallons necessary to cover the bottom of the pool.