Bunuel wrote:
Jack went up a hill to fetch a cylindrical pail of water. He filled the pail completely with 112π cubic centimeters of water, but then fell down, spilling half of the water out. At the bottom of the hill, Jack rested and discovered that the level of the remaining water was 3.5 cm below the top of the pail. What is the diameter of the circular base of the pail?
A. 3.0 cm
B. 4.0 cm
C. 4√2 cm
D. 8.0 cm
E. 8√2 cm
Since the pail has ½ of the water left and the water was 3.5 cm below the top of the pail, the height of the water in the pail is also 3.5 cm (counting from the bottom of the pail). The full height of the pail is 2 x 3.5 = 7 cm. Since we are given that the full capacity of the pail is 112π cubic centimeters, we can use the formula V = πr^2h to find the radius of the pail:
V = πr^2h
112π = πr^2(7)
16π = πr^2
16 = r^2
r = 4
Since the radius of the pail is 4 cm, the diameter of the pail is 2 x 4 = 8 cm.
Answer: D
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