[GMAT math practice question]
Water enters a cylindrical barrel at a constant speed of 500 cm^3/min, and the height of the barrel increases at a constant speed of 10 cm per minute. What is the approximate radius of the barrel, in centimeters?
A. 1
B. 2
C. 3
D. 4
E. 5
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Water enters a cylindrical barrel at a constant speed
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Max@Math Revolution
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Max@Math Revolution
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=>
Let r be the radius of the barrel.
The area of the water surface 3.14*r2.
The volume of water poured in 1 minute is 10*3.14*r^2.
Then, 10*3.14*r^2 = 500 or 31.4*r^2 = 500.
r^2=500/31.4 ~16.
Thus, the radius is approximately 4 cm.
Therefore, the answer is D.
Answer: D
Let r be the radius of the barrel.
The area of the water surface 3.14*r2.
The volume of water poured in 1 minute is 10*3.14*r^2.
Then, 10*3.14*r^2 = 500 or 31.4*r^2 = 500.
r^2=500/31.4 ~16.
Thus, the radius is approximately 4 cm.
Therefore, the answer is D.
Answer: D
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The rate the water enters a cylinder is the area of the circular base of the cylinder times the rate the height increases. Since the area of the circular base of the cylinder is πr^2, we have:Max@Math Revolution wrote:[GMAT math practice question]
Water enters a cylindrical barrel at a constant speed of 500 cm^3/min, and the height of the barrel increases at a constant speed of 10 cm per minute. What is the approximate radius of the barrel, in centimeters?
A. 1
B. 2
C. 3
D. 4
E. 5
500 = πr^2 x 10
50/Ï€ = r^2
√(50/π) = r
Since π is approximately 3, then 50/π is between 16 and 17. Let's round it down to 16, so we have:
r ≈ √16 = 4
Answer: D
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