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

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Math Expert
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135629 [0], given: 12705

If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink]

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30 Nov 2017, 22:57
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81% (01:03) correct 19% (01:35) wrong based on 20 sessions

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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
[Reveal] Spoiler: OA

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Kudos [?]: 135629 [0], given: 12705

Manager
Joined: 17 Oct 2016
Posts: 150

Kudos [?]: 38 [0], given: 89

Location: India
Concentration: Operations, Strategy
GPA: 3.7
WE: Design (Real Estate)
If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink]

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30 Nov 2017, 23:28
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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Kudos [?]: 38 [0], given: 89

VP
Joined: 22 May 2016
Posts: 1126

Kudos [?]: 402 [0], given: 645

If a rectangular block that is 4 inches by 4 inches by 10 inches is p [#permalink]

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01 Dec 2017, 10:01
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):

$$90\pi - 160$$

Kudos [?]: 402 [0], given: 645

If a rectangular block that is 4 inches by 4 inches by 10 inches is p   [#permalink] 01 Dec 2017, 10:01
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