Math CentralQuandaries & Queries


Question from Charles:

I need to calculate the external wall and top sqft surface area of a tank 54ft od x 15ft high with a dome top 54ft od x 8ft high.

Hi Charles,

The wall without the cap is the surface of a cylinder of diameter 54 feet and height 15 feet. You can imagine slicing the wall from bottom to top and rolling it out flat to form a rectangle of height 15 feet and length the circumference of the circular top of the cylinder. The circumference of a cylinder is π times the diameter so the rolled out rectangle is 54 π feet long. Hence its area is

15 × 54 π = 810 π square feet.

If the dome is part of a circle then its surface area can be found using calculus. For your cap I got a surface area of

432 π square feet.

Thus the total surface area is 810 π + 432 π = 1242 π square feet or approximately 3902 square feet.


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