If the radius of a sphere is increased by 2 cm, its surface area is increased by 464π cm². What is the radius of the original sphere? 

28 cm

When radius = r, then Surface area of a sphere = 4$\pi$r²

Now radius = (r + 2)cm

Then, surface area becomes = 4$\pi$(r + 2)²

                                              = 4$\pi$ (r² + 4 + 4r)

                                              = 4$\pi$r² + 16$\pi$ + 16$\pi$r

Change in surface area = 4$\pi$r² + 16$\pi$ + 16$\pi$r - 4$\pi$r²

⇒ 16$\pi$r + 16$\pi$ = 464$\pi$

⇒ 16r = 448

⇒ r = 28 cm