Question

Gas is being pumped into a spherical balloon at the rate of 30 ft/min. Then the rate at which the radius
increases when its radius reaches the value 15 ft is
​

Answer 1

Hey Dear,

◆ Answer -

dr/dt = 0.0106 ft/min

◆ Explaination -

# Given -

dV/dt = 30 ft³/min

r = 15 ft

# Solution -

Volume of balloon is given by -

V = 4π/3 r³

Differentiating w.r.t. t,

dV/dt = 4π/3 × 3r² × dr/dt

30 = 4×3.142/3 × 3 × 15² × dr/dt

dr/dt = 30 / (4×3.142×225)

dr/dt = 0.0106 ft/min

Hence, rate of increase of radius of ballon is 0.0106 ft/min.

Thanks dear...