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The inside dimensions of a rectangular wooden box are 6

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Manager
Joined: 12 Jul 2006
Posts: 67
Location: Boston
Followers: 1

Kudos [?]: 5 [0], given: 0

The inside dimensions of a rectangular wooden box are 6 [#permalink]  04 Nov 2006, 09:46
The inside dimensions of a rectangular wooden box 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 canisters 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

I will post the OA later.
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Good is the greatest enemy of great.

Director
Joined: 01 Oct 2006
Posts: 500
Followers: 1

Kudos [?]: 18 [0], given: 0

Now the base can have dimensions of 6*8,8*10,or6*10 so the radius of the cylinder can either 3 or 4 . So the volume can be either 90 pi or 96 pi.
Thus my pick B.
Manager
Joined: 03 Nov 2006
Posts: 161
Followers: 2

Kudos [?]: 3 [0], given: 0

Can't the radius also be 5? since one of the sides is 10...
Manager
Joined: 29 Aug 2006
Posts: 157
Followers: 1

Kudos [?]: 4 [0], given: 0

hosam wrote:
Can't the radius also be 5? since one of the sides is 10...

I labored over the same question the first time I saw this one.
The radius cannot be 5 unless 2 sides of the box have a dimension of 10.
If you draw the figure , it will make sense to you.
You can have a canister of diameter 8 which will use the face of 8X10 for its base and 6 for its hieght.
or
you can have a canister of diameter 6 which can use the face of either 6X8 or 6X10 for its base and the third dimension for its hieght.

Calculating volume , canister using base of 8X10 will have largest volume.
Hence diameter 8 or radius 4.
Hope that helps.
VP
Joined: 25 Jun 2006
Posts: 1176
Followers: 2

Kudos [?]: 68 [0], given: 0

you just need to calculate 3 volumes and decide what is the largest volume with 3 difference bases. then u can find the answer.
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