Monyberumen wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?
A. √10/2
B. √10
C. 4
D. 5
E. 10
Let's examine what occurs in a
1-hour period
The volume of water increases by 22 cubic meters.
The height of the water increases by 0.7 meters.
So, we need to find the radius of a
0.7 meter high cylinder that has a volume of
22 cubic meters.
Volume = (pi)(radius²)(height)
22 = (pi)(radius²)(
0.7)
IMPORTANT: notice that (pi)(0.7) = approximately 2.2So, we get: 22 ≈ (2.2)(radius²)
Divide both sides by 2.2: 10 ≈ radius²
Solve: radius ≈ √10
Answer: B
Cheers,
Brent
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