Question

The radius of a balloon is increasing at the rate of 10cm/sec.at what rate is the surface area of the balloon increasing when the radius is 15cm

Answer 1

Answer:

The answer is 1200π cm/sec.

Step-by-step explanation:

Given data:

dr/dt = 10cm/s  

Radius "r" = 15 cm

Surface area of sphere = 4​πr^2  

ds/dt = d/dt 4​πr^2

= 4​π x 2r x dr/dt

= 8π x 15 x 10  

= 1200π cm/sec

Thus the rate at which the surface area of the balloon increasing is 1200π cm/sec.