Question

What is the ratio of the volume of a cube to that of a sphere which will fit inside it?

Answer 1

Ratio of sphere

 `=1/2 xx "side of cube"`

`r = a/2`

Now,

Volume of cube `v_1 = a^3`

Volume of sphere

`v_2 = 4/3 pir^3`

    `=4/3 pi(a/2)^3`

    `=4/3 pi a^3 / 8`

`v_2 = 1/6pia^3`

The ratio of their volumes

`v_1 :v_2 = a^3 :1/6 pia^3`

`v_1 /v_2 = a^3/(1/6 pia^3)`

      `=6/pi`

Hence, `v_1 :v_2 = 6 : pi`