A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the i

Question

faust18 [17]

3 years ago

9

A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the i

nstant the radius is 30 cm? A. 5/(36pi)cm/min
B. 2/(18pi)cm/min
C. 4/(9pi)cm/min
D. 7/(24pi)cm/min

Mathematics

1 answer:

Burka [1] · Answer 1 · 2021-12-21T02:30:30+03:00

Burka [1]3 years ago

7 0

The volume of the sphere is expressed in the formula V = 4/3 pi r^3. The rate of change of volume is determined by differentiating the formula: dV/dt = 4pi r^2 dr/dt. When we substitute 500 cm3/min as dV/dt and 30 cm as r. Then dr/dt is equal to 0.0442 cm/min