Answer:
6.28 gallons
Step-by-step 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:
[tex]a=4 \pi r^2[/tex]
thus, the area of half a sphere is:
[tex]a=2 \pi r^2[/tex]
we know that the radius is:
[tex]r=20ft[/tex]
we substitute this to find the area of the half sphere (the area they need to paint):
[tex]a=2\pi (20ft)^2\\a=2(3.1416) (400ft^2)\\a=2,513.27ft^2[/tex]
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:
[tex]\frac{2,513.27ft^2}{400ft^2} =6.28[/tex]
6.28 gallons of paint are needed.
