Question

The surface area of a sphere is 113.04 mm2. What is the volume of the sphere? Use 3.14 for π and round to the nearest hundredth.

Answer 1

By definition, the surface area of the sphere is given by:

`A = (4) * ( \pi ) * (r ^ 2)`
Where,
r: sphere radio
Clearing r we have:

`r = √(A / (4 * \pi ))`
Substituting values:

`r = √(113.04 / (4 * 3.14 ))`

`r = 3 mm`
Then, the volume of the sphere is given by:

`V = (4/3) * (\pi) * (r ^ 3)`
Substituting values we have:

`V = (4/3) * (3.14) * (3 ^ 3) V = 113.04 mm ^ 3`
Answer:
the volume of the sphere is:

`V = 113.04 mm ^ 3`

Answer 2

volume of the sphere will be 113.04 mm³

Explanation:

Surface area of a sphere is represented by

A = 4πr²

r² =
`(A)/(4\pi )`

`r=\sqrt{(A)/(4\pi ) } =\sqrt{(113.04)/(4*(3.14)) }=√(9)=3mm`

and volume of the sphere is

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

=
`(4)/(3)\pi (3)^(3)`

= 4π × 9

= 36π

= 36 (3.14)

= 113.04 mm³

Therefore, volume of the sphere will be 113.04 mm³