The surface area of a sphere is 25$$\pi$$ cm². The volume of the sphere is:​

Correct option is D

Given:

Surface area of the sphere = 25π cm²

Concept Used:

Surface area of a sphere: A = 4πr²
Volume of a sphere: V = ($$\frac{4}{3}$$​)πr³

Formula Used:

A = 4πr²
V = ($$\frac{4}{3}$$​)πr³

Solution:

Given that the surface area A = 25π.
Using the formula for surface area:
A = 4πr²
25π = 4πr²
25 = 4r²
r² = 25 / 4
​$$r² = \frac{25}{4}\\\ \\r = \frac{5}{2}$$​​
Now, use the radius to calculate the volume V:
​$$V = (\frac{4}{3})πr³ \\\ \\V = (\frac{4}{3})π(\frac{5}{2})³ \\\ \\V = (\frac{4}{3})π × \frac{125}{8 }\\\ \\V = \frac{500}{24 }π \\\ \\V = \frac{125}{6} π cm³$$​​