Question

What is the volume of a sphere with a surface area of 25π yd2?

Answer 1

V=11.75 Thats the volume

Answer 2

The volume of sphere is:

65.4167 yd^3

Explanation:

We are given surface area of sphere as:

`Area=25\pi\ \text{yd^2}`

We know that the surface area of sphere of radius ''r'' is given by the formula:

`Area=4\pi r^2`

i.e. we have:

`4\pi r^2=25\pi\\\\i.e.\\\\r^2=(25)/(4)\\\\\\r^2=(\ddfrac{5}{2})^2\\\\i.e.\\\\r=\pm (5)/(2)`

As we know that the radius of a circle can't be negative.

Hence,

`r=(5)/(2)\ \text{yd}`

Now the volume of sphere is given by:

`Volume=(4)/(3)\pi r^3\\\\i.e.\\\\Volume=(4)/(3)\pi ((5)/(2))^3\\\\i.e.\\\\Volume=65.4167\ \text{yd^3}`

Volume of sphere is:

65.4167 yd^3