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