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The diameter and the height of a circular cylinder are 20 feet and 4 f
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14 Feb 2025, 01:25
14 Feb 2025, 01:25
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The diameter and the height of a circular cylinder are 20 feet and 4 feet respectively. What is the volume of water, in gallons, if the given cylinder is filled to a height of 3 feet and 6 inches? ( 1 foot $=12$ inches; 1 gallon $=231$ cubic inches $)$
(A) $\(\frac{56700}{7}\)$
(B) $\(\frac{57600}{7}\)$
(C) $\(\frac{58600}{7}\)$
(D) $\(\frac{58700}{7}\)$
(E) $\(\frac{59600}{7}\)$
(A) $\(\frac{56700}{7}\)$
(B) $\(\frac{57600}{7}\)$
(C) $\(\frac{58600}{7}\)$
(D) $\(\frac{58700}{7}\)$
(E) $\(\frac{59600}{7}\)$
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Re: The diameter and the height of a circular cylinder are 20 feet and 4 f
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08 Mar 2025, 04:47
08 Mar 2025, 04:47
Expert Reply
As diameter is twice the radius, if the diameter of the base of the cylinder is 20 feet, its radius is 10 feet $\(=120\)$ inches ( $\(=r\)$ say ) ( 1 feet $\(=12\)$ inches ).
The level/height at which the cylinder to be filled is 3 feet 6 inches $\(=3 \times 12+6=36+6=42\)$ inches ( $\(=\mathrm{h}\)$ say).
Note: - Though the original height of the cylinder is 4 feet, but as the cylinder is to be filled up to 3 feet 6 inch height, the height while calculating the volume would be considered as 3 feet 6 inches only.
So, the volume of water in cylinder is $\(\pi \mathrm{r}^2 \mathrm{~h}=\frac{22}{7} \times(120)^2 \times 42=1900800\)$ cubic inches which is same as $\(\frac{1900800}{231}=\frac{57600}{7}\)$ gallon (Using 1 gallon $\(=231\)$ cubic inches)
Hence the answer is (B).
The level/height at which the cylinder to be filled is 3 feet 6 inches $\(=3 \times 12+6=36+6=42\)$ inches ( $\(=\mathrm{h}\)$ say).
Note: - Though the original height of the cylinder is 4 feet, but as the cylinder is to be filled up to 3 feet 6 inch height, the height while calculating the volume would be considered as 3 feet 6 inches only.
So, the volume of water in cylinder is $\(\pi \mathrm{r}^2 \mathrm{~h}=\frac{22}{7} \times(120)^2 \times 42=1900800\)$ cubic inches which is same as $\(\frac{1900800}{231}=\frac{57600}{7}\)$ gallon (Using 1 gallon $\(=231\)$ cubic inches)
Hence the answer is (B).
gmatclubot
Re: The diameter and the height of a circular cylinder are 20 feet and 4 f [#permalink]
08 Mar 2025, 04:47
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