Cylinder

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vishugogo: Master | Next Rank: 500 Posts; Posts: 131; Joined: Tue Aug 30, 2011 4:50 am; Location: India; Thanked: 28 times; Followed by:6 members

Cylinder

by vishugogo » Fri Oct 18, 2013 11:33 am

A cylindrical piece of wood will be cut into identical cubes. The diameter of the cylinder is 6âˆš2 ft and the height is 16 ft. If the edge of the cubes must be at least 4 ft, what is the greatest total volume of the resulting cubes?

a) 256 ft3
b) 375 ft3
c) 432 ft3
d) 459 ft3
e) 496 ft3

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Source: Beat The GMAT — Problem Solving | Fri Oct 18, 2013 11:33 am

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by [email protected] » Fri Oct 18, 2013 12:24 pm

Hi vishugogo,

This question has some interesting twists to it (and one minor problem with the way that it's written - which I'll point out in a moment).

We're given the dimensions of the cylinder and we're asked about cutting it into identical CUBES, with an edge of AT LEAST 4 (which means that there will be a bunch of unused cylinder "space" when we cut it up). We're told to find the biggest volume of the resulting cubes.

**I think that the *intent* of this question is the the edges of the cube are supposed to be integers, and I'm going to present a solution based on that assumption. The largest possible volume of the cubes is not actually listed here (it would require that the edges be non-integers).

If you draw the BASE of a cylinder, you'll see a circle. Since the diameter = 6âˆš2, we can draw a square "around" that line; that square has sides = 6.

Since we're dealing with cubes, the cube would be 6x6x6. The cylinder is tall enough for us to put 2 of those cubes into it.

Total Volume = 6x6x6 x2 = 216 x 2 = 432

Final Answer: C

**IF the edges of the cubes could be non-integers, then you could fit 3 cubes in with edges = 5.333333333.
These cubes would have a volume of (16/3)^3 = about 151.7
151.7 x 3 = about 455
This is the actual maximum volume**

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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shinys: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Mon Jul 06, 2009 2:08 am

by shinys » Sat Oct 19, 2013 5:14 am

Hi Rich,
Can you please help me understand how we can tell that the side of the square is 6 with the diameter of the base being 6âˆš2?

Thanks.

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riz_gmat: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Thu Sep 26, 2013 9:05 pm; Thanked: 5 times

by riz_gmat » Sat Oct 19, 2013 9:58 am

shinys wrote:Hi Rich,
Can you please help me understand how we can tell that the side of the square is 6 with the diameter of the base being 6âˆš2?

Thanks.

Hi shinys,

If you draw a square inside a circle, the diagonal of the square will be same as the diameter of the circle, here diameter = 6âˆš2 , for a square, if diagonal = aâˆš2 , the sides of square = a
Hence sides of square = 6 in this case.