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A container in the shape of a right circular cylinder has an inside b
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12 May 2021, 06:26
12 May 2021, 06:26
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A container in the shape of a right circular cylinder has an inside base diameter of 10 centimeters and an inside height of 6 centimeters. This cylinder is completely filled with fluid. All of the fluid is then poured into a second right circular cylinder with a larger inside base diameter of 14 centimeters. What must be the minimum inside height, in centimeters, of the second container?
A. \(\frac{5}{\sqrt{7}}\)
B. \(\frac{7}{5}\)
C. \(5\)
D. \(\frac{150}{49}\)
E. \(2 \sqrt{7 }\)
A. \(\frac{5}{\sqrt{7}}\)
B. \(\frac{7}{5}\)
C. \(5\)
D. \(\frac{150}{49}\)
E. \(2 \sqrt{7 }\)
Re: A container in the shape of a right circular cylinder has an inside b
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12 May 2021, 06:39
12 May 2021, 06:39
1
Volume contained by 1st cylinder = \(π \)\(r^2\)h
= \(π\)\((5)^2\)*6
= 150 \(π\)
Since 1st cylinder was full by the fluid, Hence, the volume of fluid will be the same.
For the minimum height, the volume of the fluid should be same as the 2nd cylinder.
150 \(π\) = \(π\)\((7)^2\)*h
h =\( \frac{150}{49}\)
Hence, D
= \(π\)\((5)^2\)*6
= 150 \(π\)
Since 1st cylinder was full by the fluid, Hence, the volume of fluid will be the same.
For the minimum height, the volume of the fluid should be same as the 2nd cylinder.
150 \(π\) = \(π\)\((7)^2\)*h
h =\( \frac{150}{49}\)
Hence, D
gmatclubot
Re: A container in the shape of a right circular cylinder has an inside b [#permalink]
12 May 2021, 06:39
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