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If a rectangular block that is 4 inches by 4 inches by 10 in [#permalink]
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Question Stats: 100% (01:05) correct 0% (00:00) wrong based on 6 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 Director Joined: 20 Apr 2016
Posts: 824
WE: Engineering (Energy and Utilities)
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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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