Question

21. What is the exact volume of a sphere whose diameter is 14 cm? Show your work.

Answer 1

The exact volume of a sphere is
`V=1437cm^3`

Explanation:

Given that the diameter of a sphere is 14cm.

That is d=14

First find the radius of the sphere with diameter

`r=(d)/(2)`

`r=(14)/(2)`

Therefore r=7cm

Now to find the volume of the sphere:

`V=(4)/(3)\pi r^3cm^3`

`V=(4)/(3)(22)/(7)(7)^3` (here
`\pi=(22)/(7)` and r=7)

`V=(4)/(3)(22)(7)^2`

`V=(4)/(3)(22)(49)`

`V=(4)/(3)(1078)`

`V=(4312)/(3)`

`V=1437.33cm^3`

Therefore the volume of the given sphere is
`V=1437.33cm^3`

The exact volume of a sphere is
`V=1437cm^3`