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# Brain Stuck A cube and cylinder are equal in height. Does

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Eternal Intern
Joined: 07 Jun 2003
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Brain Stuck A cube and cylinder are equal in height. Does [#permalink]  11 Jul 2003, 19:33
Brain Stuck

A cube and cylinder are equal in height. Does the cube hold more water than the cylinder?

( 2) The diameter of the cylinder is equal to the base of the cube.

Just use that data.

VT
Manager
Joined: 18 Jun 2003
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No, the cylinder holds pi/4 x the volume of the cube
SVP
Joined: 03 Feb 2003
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The diameter (D) of the cylinder is equal to the base of the cube.

The volume of the cube is D^3
The volume of the cylinder is (pi/4)D^3

pi/4<1

So, the cube holds more
Manager
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there is another solution:
imagine first cube and then cylindre in it - the answer is clear.
Intern
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definitely the cube [#permalink]  14 Jul 2003, 10:17
If the side of the cube = S, and the radius of the cylinder = r, and the equal height = h,

Since the side of the tube is equal to the height of the cube, then S=h,
Since the diameter of the cylinder equal to the base of the cube which is S, then the radius of the cynlinder is (S/2)

then the volume of the cube = S^2 * h
the volume of the cylinder = 3.14 * (s/2)^2 * h = (3.14/4) * S^2 *h

Now it is very clear that the volume of the cube is larger since S^2*h is definitely larget than 3/4 of (3.14/4) * S^2 *h.

Hope this is clear enough.

Good luck.
definitely the cube   [#permalink] 14 Jul 2003, 10:17
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