SOLUTION: An observatory has the shape of a right circular cylinder topped by a hemisphere. The radius of the cylinder is 10 ft and its altitude measures 24 ft (Alexander & Koeberlein, 2003)

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Question 107577: An observatory has the shape of a right circular cylinder topped by a hemisphere. The radius of the cylinder is 10 ft and its altitude measures 24 ft (Alexander & Koeberlein, 2003).

A. What is the approximate surface area of the observatory? Round to the nearest foot.
Show all work to receive full credit. (Hint: Remember the top and bottom of the
cylinder will not be painted, so do not include them in your surface area.)

B. If 1 gallon of paint covers 300 ft2, how many gallons are needed to paint the surface if it requires three coats? Round up to the nearest gallon. Show all work to receive full credit.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!
First let's deal with the area of the hemisphere dome. The surface area of a sphere is given by , but this is a hemisphere, so we only need half of that, or .

Since we only need to compute to the nearest square foot, should be a close enough approximation. Since the dome fits on top of the 10 foot radius cylinder, the hemisphere radius must also be 10 feet.

The cylinder part is easy if you consider cutting it all the way up the side and then flattening it out so that you will have a rectangle that is the cylinder altitude on one side and the cylinder circumference on the other.

Since , the circumference of the cylinder is 62.8 ft.

Then the surface area of the cylinder must be

Adding the cylinder surface to the dome surface and rounding gives:

rounded to the nearest square foot.

Each gallon of paint covers , so which is 7.12 gallons, but rounded UP is 8 gallons.