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# There are two right circular cylinders A and B. The height and the dia

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
There are two right circular cylinders A and B. The height and the dia  [#permalink]

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16 Oct 2018, 04:45
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25% (medium)

Question Stats:

76% (01:36) correct 24% (01:29) wrong based on 61 sessions

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There are two right circular cylinders A and B. The height and the diameter of cylinder B are each twice those of cylinder A. If the capacity of cylinder A is 10 barrels, what is the capacity of cylinder B, in barrels?

(A) 36
(B) 40
(C) 60
(D) 80
(E) 100

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Posts: 210
Re: There are two right circular cylinders A and B. The height and the dia  [#permalink]

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16 Oct 2018, 06:22
Volume of larger barrel = $$π (2r)^2 * 2h = 8πr^2$$

Capacity of $$πr^2h$$ = 10 barrels
Capacity of $$8πr^2$$ = 80 barrels
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Re: There are two right circular cylinders A and B. The height and the dia  [#permalink]

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17 Oct 2018, 19:07
Bunuel wrote:
There are two right circular cylinders A and B. The height and the diameter of cylinder B are each twice those of cylinder A. If the capacity of cylinder A is 10 barrels, what is the capacity of cylinder B, in barrels?

(A) $36 (B)$40
(C) $60 (D)$80
(E) \$100

We can let h and r be the height and radius of cylinder A. Thus we have πr^2 * h = 10. Since the height and the diameter of cylinder B are each twice those of cylinder A, we have the height and radius of cylinder B as 2h and 2r, respectively (notice that if the diameter of cylinder B is twice that of cylinder A, its radius is also twice that of cylinder A). So the capacity (or volume) of cylinder B is:

V = π(2r)^2 * (2h) = π(4r^2) * (2h) = 8πr^2 * h

Since πr^2 * h = 10, the capacity of cylinder B is 8(10) = 80.

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Re: There are two right circular cylinders A and B. The height and the dia   [#permalink] 17 Oct 2018, 19:07
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