A cylindrical piece of wood will be cut into identical cubes. The diameter of the cylinder is 6√2 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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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 = 6√2, 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
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 = 6√2, 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
Hi shinys,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 6√2?
Thanks.
If you draw a square inside a circle, the diagonal of the square will be same as the diameter of the circle, here diameter = 6√2 , for a square, if diagonal = a√2 , the sides of square = a
Hence sides of square = 6 in this case.
