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16 Nov 2021, 09:29
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What is the volume of a right cylindrical can X?
(1) If the height of can X were equal to the radius of the base of can X, the volume of the new cylinder would have been half of the volume of can X
(2) If the radius of the base of can X were equal to height of can X, the volume of the new cylinder would have been four times the volume of can X
(1) If the height of can X were equal to the radius of the base of can X, the volume of the new cylinder would have been half of the volume of can X
(2) If the radius of the base of can X were equal to height of can X, the volume of the new cylinder would have been four times the volume of can X
16 Nov 2021, 09:29
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Official Solution:
What is the volume of a right cylindrical can X?
\(Volume=\pi r^2h\), where \(r\) is the radius of the circular base and \(h\) is the height,
(1) If the height of can X were equal to the radius of the base of can X, the volume of the new cylinder would have been half of the volume of can X
The above means that \(\pi r^2h=2*(\pi r^2*r)\). This gives \(h=2r\). Not sufficient.
(2) If the radius of the base of can X were equal to height of can X, the volume of the new cylinder would have been four times the volume of can X
The above means that \(4*(\pi r^2h)=\pi h^2*h\). This also gives \(h=2r\). Not sufficient.
(1)+(2) We only know the ratio of height to the radius but we know nothing about actual lengths, so we cannot get the volume. Not sufficient.
Answer: E
What is the volume of a right cylindrical can X?
\(Volume=\pi r^2h\), where \(r\) is the radius of the circular base and \(h\) is the height,
(1) If the height of can X were equal to the radius of the base of can X, the volume of the new cylinder would have been half of the volume of can X
The above means that \(\pi r^2h=2*(\pi r^2*r)\). This gives \(h=2r\). Not sufficient.
(2) If the radius of the base of can X were equal to height of can X, the volume of the new cylinder would have been four times the volume of can X
The above means that \(4*(\pi r^2h)=\pi h^2*h\). This also gives \(h=2r\). Not sufficient.
(1)+(2) We only know the ratio of height to the radius but we know nothing about actual lengths, so we cannot get the volume. Not sufficient.
Answer: E
