SOLUTION: A company has a right cylindrical storage tank for storing natural gas. The tank measures 20 feet wide by 60 feet high. The company estimates that it will cost $2.00 per square f

Algebra ->  Circles -> SOLUTION: A company has a right cylindrical storage tank for storing natural gas. The tank measures 20 feet wide by 60 feet high. The company estimates that it will cost $2.00 per square f      Log On


   

Question 85588: A company has a right cylindrical storage tank for storing natural
gas. The tank measures 20 feet wide by 60 feet high.
The company estimates that it will cost $2.00 per square foot to
paint the tank. Which of the following expressions could be used
to determine the total cost to paint the top and the side of the tank?
A. %281200pi+%2B+100pi%29%282.00%29
B.
%281200pi+%2B+100pi%29%2F2.00
C. %281200pi+%2B+200pi%29%282.00%29
D.
%281200pi+%2B+200pi%29%2F2.00
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the surface area of the lateral side, we can "roll" out the lateral side like this


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So the area (which now represents a rectangle) is

2%2Api%2Ar%2Ah

the part 2%2Api%2Ar represents the circumference of the circle at the top and the h is the height. So imagine the lateral surface area looking like this:

Here is the lateral side rolled out

and here is the surface area of the top of the cylinder

pi%2Ar%5E2 which represents the area of a circle

So the surface area of the side and the top is:

2%2Api%2Ar%2Ah%2Bpi%2Ar%5E2