Question

20 POINTS BECAUSE THIS IS EVIL! And due at 8am tomorrow, BTW.

Part A: What is the total surface area of the tower? Round your answer to the nearest hundredth.

Part B: Another tower is constructed by placing the original tower on top of another cylinder with a height of 18 inches and a radius of 54 inches. What is the total surface area of the new tower? Round your answer to the nearest hundredth.

I know the end result of the entire problem is 14,249.5in squared, but I can't figure out how to get to that answer. Could anyone help me?

Answer 1

1) For this part, You need to calculate C.S.A of small cylinder & T.S.A of larger cylinder, 
 C.S.A. of small cylinder = 2πrh = 2 * 3.14 * 18 * 18 = 2034.72
 
 T.S.A. of larger cylinder = 2πr(h + r) = 2 * 3.14 * 36 (18 + 36) = 6104.16

So, Surface area of out original figure = 6104.16 + 2034.72 = 8138.88 in²

2) Now, For surface area of the new figure, 
 C.S.A of smaller + C.S.A of middle + T.S.A of larger cylinder

C.S.A of smaller = 2034.72

C.S.A of middle = 2πrh = 2*3.14 * 18* 36 = 4069.44

T.S.A of larger = 2πr(h + r) = 2 * 3.14 * 54 (18 + 54) = 8138.88

Total Area = 2034.72 + 4069.44 + 8138.88 = 14243.04 in²

Hope this helps!