SOLUTION: A large storage building is in the shape of a hemisphere. If it took 40 liters of paint to cover the floor, how many liters can one expect to need to paint the exterior of the buil

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Question 1195301: A large storage building is in the shape of a hemisphere. If it took 40 liters of paint to cover the floor, how many liters can one expect to need to paint the exterior of the building
Found 3 solutions by Theo, josgarithmetic, math_tutor2020:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
a hemisphere is half a sphere.
the base of the hemisphere is a circle.
the area of a circle is equal to pi * r^2.
r is the radius of the circle.
the surface area of a sphere is equal to 4 * pi * r^2.
the surface area of a hemisphere is equal to 2 * pi * r^2 (half the surface area of a sphere).
the ratio of the surface area of a hemisphere to the area of a circle is equal to 2 * pi * r^2 / pi * r^2 = 2 / 1.
if 40 liters of paint were required to paint the floor, then 80 liters of paint would be required to paint the exterior of the building.
this assumes the floor dimensions are to the exterior of the building rather than the interior, since the thickness of the building structure would need to be taken into consideration as well.
that's what i think is your solution.




Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
pi%2Ar%5E2 area corresponds to 40 liters of paint.

4pi%2Ar%5E2 would be whole sphere area, but the building is hemisphere
so 2pi%2Ar%5E2 would be the area needing to be painted.

%282pi%2Ar%5E2%29%2F%28pi%2Ar%5E2%29=2
Ratio of the exterior paint to the floor paint is 2;
therefore 80 liters of paint needed for the exterior.

Answer by math_tutor2020(3835) About Me  (Show Source):
You can put this solution on YOUR website!

To paraphrase the other tutors: You need twice as much paint to cover the ceiling, compared to the floor.

ceiling = 2*floor
ceiling = 2*(40 liters)
ceiling = 80 liters