Question

if the diameter of a sphere is equal to the side of a cube,find the ratio of their volumes​

Answer 1

The ratio of volume of sphere to volume of cube is "$\dfrac{\pi }{6}$: 1".

Step-by-step explanation:

Let diameter of the sphere = d = side of the cube

∴ Radius of the sphere(r) = $\dfrac{d}{2}$

Volume of sphere =$\dfrac{4}{3}\pi\[r^{3}$

=$\dfrac{4}{3}\pi\dfrac{d}{2}r^{3}$

= $\dfrac{\pi }{6}d^{3}$

And,

Volume of the cube = $d^{3}$

∴ The ratio of volume of sphere to volume of cube

= $\dfrac{\pi }{6}$$d^{3}$ :  $d^{3}$

= [tex]\dfrac{\pi }{6} : 1

Hence, the ratio of volume of sphere to volume of cube is [tex]\dfrac{\pi }{6} : 1.

Answer 2

Answer:

the answer is 6:pie.............