Question

The volume of a sphere is 3,500 pi m cubed. What is the surface area of the sphere to the nearest square meter?

Answer 1

`2390 {m}^(2)`

Explanation:

The formula for calculating the volume of a cylinder is

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

It was given that the volume is 3,500π m³

We equate the formula to this value to get:

`(4)/(3) \pi {r}^(3) = 3500\pi`

`{r}^(3) = (3 * 3500\pi)/(4\pi)`

`{r}^(3) = 2625`

`r = \sqrt[3]{2625}`

`r = 13.79`

The area of a sphere is given by:

`Area=4 \pi{r}^(2)`

`Area=4 * \pi * {13.79}^(2)`

`Area=2389.67`

Therefore the area is approximately 2390m² to the nearest square unit.