Question

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The diameter and height of a cylinder are equivalent to the edge lengths of a cube. Which figure has a greater volume?
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a. They have the same volume.

b.The cube

c.The cylinder

d.There is not enough information.

Answer 1

The cube has a greater volume

Explanation:

The volume of a cylinder of height H and diameter radius D has a volume given by the area of the base (a circle of radius D/2), and the height H.

Notice also that the cube has the same edge dimensions of the cylinder, so as a cube has equal length, width, an height, that means that the height H of the cylinder must also be the same dimension of its diameter (H = D)

So we can refer all quantities as D:

Volume of the cylinder =
`\pi\,r^2\,h=\pi\,((D)/(2))^2\,(D)=(\pi)/(4) D^3`

while the volume of a cube of side "D" is :

Volume of the cube =
`D^3`

Notice as well that the number
`\pi` is smaller than 4, therefore the fraction
`(\pi)/(4) = 0.7854` that multiplies
`D^3` in the volume of the cylinder, is reducing its value.

Therefore the cube has a larger volume than the cylinder.