Official Guide Explanation:
Problem Solving #D05




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Solution and Metadata

Question: D05
Page: 20
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Rectangular Solids and Cylinders > Cylinders
Category 2: Word Problems > Geometry Problems >

Explanation: There are two cylinders to consider here. First, the actual cylindrical tank. If the tank is half full and the water reaches a height of 4 feet, the height of the tank itself must be 8 feet. Second, the cylinder of water--that is, the half of the tank that is filled. If the water has a volume of 36 π and a height of 4, we can calculate the radius of the base:

v= π r2h

36 π = π r2(4)

9 = r2

r = 3

Thus, the tank has a radius of 3 feet.

Next, the tank is turned on its side. If the radius of the tank is 3 feet, the diameter of the tank is 6 feet, meaning that the "height" of the tank, now that it's lying on its side, is 6 feet. Since the tank is half full, the height of the water is now 3 feet, choice (B).

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