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If a rectangular block that is 4 inches by 4 inches by 10 in [#permalink]
Expert's post 00:00

Question Stats: 95% (00:49) correct 5% (00:00) wrong based on 20 sessions
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) $$90\pi - 160$$
[Reveal] Spoiler: OA

_________________ Manager Joined: 26 Jan 2018
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Re: If a rectangular block that is 4 inches by 4 inches by 10 in [#permalink]
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Area of cylinder is Pi r^h

=Pi*3*3*10
=90Pi

Area of cuboid = l*b*h
=4*4*10 = 160

Volume unoccupied = 90Pi-160 VP Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
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Kudos [?]: 1340  , given: 251

Re: If a rectangular block that is 4 inches by 4 inches by 10 in [#permalink]
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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) $$90\pi - 160$$

Here,
we are required to find the volume of the un occupied portion so in that case let us take out the volume of the rectangular solid and cylinder

Volume of the rectangular solid = $$Length * Width * Height = 4 * 4 * 10 =160$$

And Total Volume of the Cylinder = $$\pi * Radius^2 * Height = \pi * 3^2 * 10 = 90\pi$$

Therefore the volume of the unoccupied portion of the cylinder = Total Volume of the Cylinder - Volume of the rectangular solid =$$\pi * 3^2 * 10 = 90\pi - 160$$
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GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests Re: If a rectangular block that is 4 inches by 4 inches by 10 in   [#permalink] 07 Jul 2018, 09:14
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