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 = [tex]\pi\,r^2\,h=\pi\,(\frac{D}{2})^2\,(D)=\frac{\pi}{4} D^3[/tex]
while the volume of a cube of side "D" is :
Volume of the cube = [tex]D^3[/tex]
Notice as well that the number [tex]\pi[/tex] is smaller than 4, therefore the fraction [tex]\frac{\pi}{4} = 0.7854[/tex] that multiplies [tex]D^3[/tex] in the volume of the cylinder, is reducing its value.
Therefore the cube has a larger volume than the cylinder.
