The inside dimensions of a rectangular wooden are...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

The inside dimensions of a rectangular wooden are...

by BTGmoderatorLU » Tue Jan 23, 2018 5:58 am

The inside dimensions of a rectangular wooden are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canister that could be used, what is the radius, in inches, of the one that has the maximum volume?

A. 3
B. 4
C. 5
D. 6
E. 8

The OA is B.

I'm confused with this PS question.

I know that the volume of a cylinder is
$$V_{cylinder}=\pi\cdot r^2\cdot h$$
But, how can I solve this question? Experts, any suggestion? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Tue Jan 23, 2018 5:58 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Jan 23, 2018 6:07 am

LUANDATO wrote:The inside dimensions of a rectangular wooden are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canister that could be used, what is the radius, in inches, of the one that has the maximum volume?

A. 3
B. 4
C. 5
D. 6
E. 8

Volume of cylinder = Ï€(radiusÂ²)(height)

There are 3 different ways to position the cylinder (with the base on a different side each time).
You can place the base on the 6x8 side, on the 6x10 side, or on the 8x10 side

If you place the base on the 6x8 side, then the cylinder will have height 10, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6).
So, the volume of this cylinder will be (Ï€)(3Â²)(10), which equals 90Ï€

If you place the base on the 6X10 side, then the cylinder will have height 8, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6).
So, the volume of this cylinder will be (Ï€)(3Â²)(8), which equals 72Ï€

If you place the base on the 8x10 side, then the cylinder will have height 6, and the maximum radius of the cylinder will be 4 (i.e., diameter of 8).
So, the volume of this cylinder will be (Ï€)(4Â²)(6), which equals 96Ï€

So, the greatest possible volume is 96Ï€ and this occurs when the radius is 4

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Wed Jan 24, 2018 9:47 am

LUANDATO wrote:The inside dimensions of a rectangular wooden are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canister that could be used, what is the radius, in inches, of the one that has the maximum volume?

A. 3
B. 4
C. 5
D. 6
E. 8

In order for the canister to stand upright in the box, the diameter of the canister must fit within the base of the box. Let's test various scenarios to determine which will provide the largest volume of the canister. Remember, the volume of a cylinder = Ï€r^2h. Keep in mind that the height of the cylindrical canister is the same as the height of the box.

Scenario 1:

The base of the box is 6 by 8 and the height is 10. Thus, the diameter of the cylinder = 6, which means the radius = 3 and the volume of the cylinder is:

V = Ï€(3)^2 x 10 = 90Ï€

Scenario 2:

The base of the box is 6 by 10 and the height is 8. Thus, the diameter of the cylinder = 6, which means the radius = 3 and the volume of the cylinder is:

V = Ï€(3)^2 x 8 = 72Ï€

Scenario 3:

The base of the box is 8 by 10 and the height is 6. Thus, the diameter of the cylinder = 8, which means the radius = 4 and the volume of the cylinder is:

V = Ï€(4)^2 x 6 = 96Ï€

Scenario 3 gives us the greatest volume, and the radius of the cylinder is 4.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
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