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# What is the volume of the largest box with a square base that can fit

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
What is the volume of the largest box with a square base that can fit  [#permalink]

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07 Sep 2018, 00:36
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:08) correct 40% (01:15) wrong based on 17 sessions

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What is the volume of the largest box with a square base that can fit into a cylindrical canister with volume 25π?

(1) The cylinder has a radius of $$\sqrt{5}$$.
(2) The height of the cylinder is 5.

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What is the volume of the largest box with a square base that can fit  [#permalink]

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07 Sep 2018, 01:32
Bunuel wrote:
What is the volume of the largest box with a square base that can fit into a cylindrical canister with volume 25π?

(1) The cylinder has a radius of $$\sqrt{5}$$.
(2) The height of the cylinder is 5.

Question: What is the volume of the largest box with a square base that can fit into a cylindrical canister with volume 25π?

To answer this question, we need only the radius or height of cylinder because we have the volume of cylinder 25π already.

For any specific cylinder the box of maximum volume can be derived as square base with diagonal equal to diameter and height equal to height of cylinder

Statement 1: The cylinder has a radius of $$\sqrt{5}$$

SUFFICIENT

Statement 2; The height of the cylinder is 5

SUFFICIENT

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What is the volume of the largest box with a square base that can fit   [#permalink] 07 Sep 2018, 01:32
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# What is the volume of the largest box with a square base that can fit

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