Question

A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder . If their heights are the same with the same base, find the ratio of their volumes

Answer 1

Assume that the length of all edges of the cube=x units
Formula for volume of cube=x³ cube unit
Due an occurrence that the cylinder is within the cube &it touches all the vertices faces of the cube.
Therefore radius of the base of the cylinder & cone & height of cylinder of a cone=x
Volume of the cylinder=π×{x/2}²×x=22/7×x³/4
11/14x³ cube unit
Volume of cone should be=1/3π{x/2)²×x=11/42 cubic unit
Required ratio=volume of cube:volume of cylinder:volume of cone
=x³:11/14x³:11/42x³=42:33:11

Answer 2

Step-by-step explanation:

Let the side of the cube = a

Since cylinder is inside the cube then the diameter and the height is equal to the side of the cube

Diameter = height of the cylinder (h) = a

Then the radius of cylinder (r) = a/2

\\ \text{Volume of the cube = }a^3\\ \text{Volume of the cylinder = } \pi r^2h=\pi\times \left (\frac a2 \right )^2\times a=\frac{\pi a^3}{4}\\ \text{Volume of the cone = } \frac13\pi r^2h=\frac13\times\pi\times \left (\frac a2 \right )^2\times a=\frac{\pi a^3}{12} Now,

Ratio of cube, cylinder and cone