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# A cylindrical pail has a radius of 7 inches and a height of 9 inches.

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
A cylindrical pail has a radius of 7 inches and a height of 9 inches. [#permalink]

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19 Mar 2018, 01:45
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A cylindrical pail has a radius of 7 inches and a height of 9 inches. If there are 231 cubic inches to a gallon, approximately how many gallons will this pail hold?

(A) 6
(B) 12/7
(C) 7.5
(D) 8.2
(E) 9
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
Re: A cylindrical pail has a radius of 7 inches and a height of 9 inches. [#permalink]

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19 Mar 2018, 01:47
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Bunuel wrote:
A cylindrical pail has a radius of 7 inches and a height of 9 inches. If there are 231 cubic inches to a gallon, approximately how many gallons will this pail hold?

(A) 6
(B) 12/7
(C) 7.5
(D) 8.2
(E) 9

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Re: A cylindrical pail has a radius of 7 inches and a height of 9 inches. [#permalink]

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19 Mar 2018, 02:16
Bunuel wrote:
A cylindrical pail has a radius of 7 inches and a height of 9 inches. If there are 231 cubic inches to a gallon, approximately how many gallons will this pail hold?

(A) 6
(B) 12/7
(C) 7.5
(D) 8.2
(E) 9

The volume of a cylinder is $$\pi * r^2 * h$$

In this problem, r = 7 and h = 9. An approximate value of $$\pi = \frac{22}{7}$$
Substituting these values, the volume of the pail is $$\frac{22}{7}* 7 * 7 * 9 = 22 * 63$$ cubic inches

Since 231 cubic inches translates to a gallon, there would be $$\frac{22 * 63}{231} = \frac{22*21}{77} = 6$$ gallons in the cylindrical pail (Option A)

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Re: A cylindrical pail has a radius of 7 inches and a height of 9 inches. [#permalink]

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20 Mar 2018, 16:54
Bunuel wrote:
A cylindrical pail has a radius of 7 inches and a height of 9 inches. If there are 231 cubic inches to a gallon, approximately how many gallons will this pail hold?

(A) 6
(B) 12/7
(C) 7.5
(D) 8.2
(E) 9

We can determine the volume of the pail:

volume = πr^2h

volume = π(7^2)(9) inches^3

So the number of gallons it will hold is:

[π(7^2)(9)]/231 = [π(7^2)(3)]/77 = [π(7)(3)]/11 = 21π/11 ≈ 65/11 ≈ 6

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Re: A cylindrical pail has a radius of 7 inches and a height of 9 inches.   [#permalink] 20 Mar 2018, 16:54
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