Question

Find the number of cubic centimeters in the volume of a sphere whose surface area is 324π cm². Leave your answer in terms of π.

Answer 1

Given, the surface area of a sphere is =
`324\pi cm^2`

The formula to find the surface area of a sphere =
`4\pi r^2`

Where, r is the radius of the sphere.

As the surface area of the sphere given, we can equate it with the formula.

So we can write the equation as,

`4\pi r^2=324\pi`

To find r, first we have to move 4 to the right side by dividing it to both sides. We will get,

`(4\pi r^2)/4 = (324\pi )/4`

`\pi r^2 = (324\pi )/4`

`\pi r^2 = 81\pi`

Now to find r, we have to move
`\pi` to the right side, by dividing it to both sides. We will get,

`(\pi r^2)/\pi =(81\pi )/\pi`

`r^2 = 81`

Now to find r, we will take square root to both sides.

`√(r^2) = √(81)`

`r = 9`

So we have got the radius of the sphere = 9cm.

Now the formula to find the volume of the sphere =
`((4)/(3))\pi r^3`

Now plugging in the value of r we will get,

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

=
`(4)/(3)\pi (9)^3`

=
`(4)/(3)\pi (729)`

=
`((4)(729\pi))/(3)`

=
`((2916\pi))/(3)`

=
`(972\pi )`

So the required volume of the sphere =
`972\pi cm^3`