Question

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Answer 1

Answer:

The cube has a greater volume

Step-by-step 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 = $\pi\,r^2\,h=\pi\,(\frac{D}{2})^2\,(D)=\frac{\pi}{4} D^3$

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 $\frac{\pi}{4} = 0.7854$ that multiplies $D^3$ in the volume of the cylinder, is reducing its value.

Therefore the cube has a larger volume than the cylinder.