Question

Find the volume of a sphere with a surface
area of 2,123.72 square meters

Answer 1

9202.77m³

Explanation:

Let's get the volume of the sphere by finding the radius using the surface area given

Surface area of a sphere = 4πr²

`2123.72 = 4 * 3.14 * {r}^(2)`

`2123.72 = 12.57 {r}^(2)`

`\frac{12.57 {r}^(2) }{12.57} = (2123.72)/(12.57)`

`{r}^(2) = 168.95`

`r = 13.0`

Volume of a sphere

`(4)/(3)\pi {r}^(3)`

`(4)/(3) * 3.14 * {13}^(3) = 9202.77 {m}^(3)`

Answer 2

To find the volume of a sphere, we can use the formula:

V = (4/3) * π * r^3
Where r is the radius of the sphere. To find the radius, we can use the surface area formula for a sphere:


A = 4 * π * r^2
So, rearranging this formula to solve for r:

r = √(A / (4 * π))
Substituting the given surface area of 2,123.72 square meters and simplifying:


r = √(2123.72 / (4 * π)) = √(532.43) = 23.06
Now that we have the radius, we can use it to find the volume of the sphere:


V = (4/3) * π * r^3 = (4/3) * π * 23.06^3 = 24,785.01 cubic meters
So the volume of a sphere with a surface area of 2,123.72 square meters is approximately 24,785.01 cubic meters