Question

How many gallons of paint are needed to paint one coat, if a gallon of paint covers 400ft squared?

Answer 1

6.28 gallons

Explanation:

first we need to find the area of a half sphere, and then find how much paint will be needed for that area.

The area of a sphere:

`a=4 \pi r^2`

thus, the area of half a sphere is:

`a=2 \pi r^2`

we know that the radius is:

`r=20ft`

we substitute this to find the area of the half sphere (the area they need to paint):

`a=2\pi (20ft)^2\\a=2(3.1416) (400ft^2)\\a=2,513.27ft^2`

now the question is how many gallons of paint are needed to paint 2,513.27 square feet.

We are told that 1 gallon covers 400 square feet

thus, we must divide 2,513.27 by 400:

`(2,513.27ft^2)/(400ft^2) =6.28`

6.28 gallons of paint are needed.