Question

The volume of a sphere is 4500π m3. What is the surface area of the sphere to the nearest square meter?

Answer 1

2827 m²

Explanation:

The equation for volume of a sphere is:

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

Using this equation and the given volume of the sphere, we can find the radius of the sphere.

Finding the Radius

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

`4500\pi = (4)/(3)\pi r^3`

Divide both sides by π

`4500=(4)/(3)(r^3)`

Multiply both sides by 3

`13500=4( r^3)`

Divide both sides by 4

`3375=r^3`

Take the cube root of both sides

`r=15`

Thus the radius of the sphere is 15m. We can use this information to find the surface area of the sphere.

Finding the Surface Area

The equation for surface area of a sphere is
`4\pi r^2`. Substituting the value we found for the radius into the equation, we find:

`SA=4\pi r^2\\SA=4\pi 15^2\\SA=4\pi 225\\SA=900\pi\\SA\approx2827$ m^2`

The surface area of the sphere, rounded to the nearest square meter, is 2827 m².