Question

The volume of a sphere is 904.32 mm^3. What is the approximate volume of a cone that has the same height and circular base with the same diameter? Use 3.14 for pi and round to the nearest hundredth.

Answer 1

`V_c=452.16\ mm^3`

Explanation:

Given that,

The volume of a sphere is 904.32 mm³.

The volume of a cone that has the same height and circular base with the same diameter is:

`V_c=(1)/(3)\pi r^2 * 2r=(2)/(3)\pi r^3`

The volume of a sphere with the same radius is:

`V_s=(4)/(3)\pi r^3=2* (2)/(3)\pi r^3`

So, the volume of sphere is :

`V_c=(V_s)/(2)\\\\V_c=(904.32 )/(2)\\\\V_c=452.16\ mm^3`

So, the volume of the cone is
`452.16\ mm^3`.