SOLUTION: Hi You are painting the surface of a silo of radius 8 ft and height 50ft. What is the total surface area to be painted. Assume the top is a hemisphere and that the silo sits on th

Question 1191506: Hi
You are painting the surface of a silo of radius 8 ft and height 50ft. What is the total surface area to be painted. Assume the top is a hemisphere and that the silo sits on the ground. Use pi = 3.14.
Thanks.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

hemisphere = half a sphere

A full sphere has this surface area
SA = 4*pi*r^2
which makes 2pi*r^2 the surface area of a hemisphere (half as much as the previous expression)

Plug in r = 8 to find...
SA = 2*pi*r^2
SA = 2*pi*8^2
SA = 128pi
is the surface area of the hemispherical portion.

The cylindrical portion involves only the lateral surface area because the base isn't painted, and the top of the cylinder is covered by the hemisphere.
We only consider the curved side.

LSA = lateral surface area
LSA of cylinder = 2*pi*r*h
LSA of cylinder = 2*pi*8*50
LSA of cylinder = 800pi

Combine the two surface area results:
hemisphere + LSA = 128pi+800pi = 928pi

That's the exact surface area needed to be painted in terms of pi.
Replace pi with 3.14 to find its approximate counterpart.
928*pi = 928*3.14 = 2,913.92

Answer: 2913.92 square feet (approximate)

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