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

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

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New post 30 Nov 2017, 22:57
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Question Stats:

80% (01:23) correct 20% (01:42) wrong based on 57 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

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

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

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New post 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):

\(90\pi - 160\)

Answer E
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If a rectangular block that is 4 inches by 4 inches by 10 inches is pl  [#permalink]

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New post 18 May 2018, 15:01
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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]

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New post 18 May 2018, 18:19
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]

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New post 18 May 2018, 23:23
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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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