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

Question

asked Oct 21, 2023 55.7k views

1 Answer

MissT · Answer 1 · 2023-10-24T17:39:03+0000

Answer:

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.

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

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

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.

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.