Gideon is blowing up a spherical beach ball. If the radius is increasing at a rate of 4 mm/sec, at what rate is the surface area of the ball changing when the radius is 15 mm?

Answer 1

Surface area of sphere is S = 4πr². Now dS/dt = 8πrdr/dt = 8π·15mm·4mm/sec = 1508 mm²/sec

Answer 2

Surface area of a sphere, S(r) = 4πr²

S '(r) = 8πr r'

r' = 4 mm/sec as given in the description

S '(15) = 8π(15)4 = 480π mm/s