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If a rectangular block that is 4 inches by 4 inches by 10 inches is p

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Bunuel
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If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink] New post   30 Nov 2017, 23:57
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If a rectangular block that is 4 inches by 4 inches by 10 inches is placed inside a right circular cylinder of radius 3 inches and height 10 inches, the volume of the unoccupied portion of the cylinder is how many cubic inches?

(A) 6π – 16
(B) 9π – 16
(C) 160 – 30π
(D) 60π – 160
(E) 90π – 160
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If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink] New post   01 Dec 2017, 00:28
E

Volume of cylinder =pi.3^2*10
=90.pi

Volume of rectangular block = 4*4*10=160

Hence unoccupied volume =90.pi-160


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If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink] New post   01 Dec 2017, 11:01
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Bunuel wrote:
If a rectangular block that is 4 inches by 4 inches by 10 inches is placed inside a right circular cylinder of radius 3 inches and height 10 inches, the volume of the unoccupied portion of the cylinder is how many cubic inches?

(A) 6π – 16
(B) 9π – 16
(C) 160 – 30π
(D) 60π – 160
(E) 90π – 160

Volume of rectangular block =
(L * W * H) = (4 * 4 * 10) = 160 cubic inches

Volume of right circular cylinder, where r = 3 and h = 10:
\(\pi r^2h = \pi(3^2)(10) = 90\pi\) cubic inches

Unoccupied space, in cubic inches, is
(cylinder volume) - (rectangular block volume):

\(90\pi - 160\)

Answer E
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If a rectangular block that is 4 inches by 4 inches by 10 inches is pl [#permalink] New post   18 May 2018, 16:01
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If a rectangular block that is 4 inches by 4 inches by 10 inches is placed inside a right circular cylinder of radius 3 inches and height 10 inches, the volume of the unoccupied portion of the cylinder is how many cubic inches?

(A) \(6\pi - 16\)

(B) \(9\pi - 16\)

(C) \(160 - 30\pi\)

(D) \(60\pi - 160\)

(E) \(90\pi - 160\)
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Re: If a rectangular block that is 4 inches by 4 inches by 10 inches is pl [#permalink] New post   18 May 2018, 19:19
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Volume Cylinder = pi * r^2 * h = pi * 3^2 * 10 = 90pi

Volume Block = 10 * 4 * 4 = 160

Volume space in cynlinder = 90pi - 160

Answer: E
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Re: If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink] New post   19 May 2018, 00:23
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carcass wrote:
If a rectangular block that is 4 inches by 4 inches by 10 inches is placed inside a right circular cylinder of radius 3 inches and height 10 inches, the volume of the unoccupied portion of the cylinder is how many cubic inches?

(A) \(6\pi - 16\)

(B) \(9\pi - 16\)

(C) \(160 - 30\pi\)

(D) \(60\pi - 160\)

(E) \(90\pi - 160\)

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Re: If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink] New post   16 Sep 2022, 11:27
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Re: If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink]
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