Calculus: Related Rates

Question

1. A spherical balloon is being inflated so that its diameter is increasing at a rate of 4 cm/min. How quickly is the volume of the balloon increasing when the diameter is 15 cm?
2. A person that is 5 m tall walks with a 1 cm/s rate towards a flag pole with a height of 17 m high. At what rate does the person’s shadow decreasing as he gets closer and closer to the flag pole?

Answer 1

Christine,

first of all m = diameter

we know m = 2r   r is radias and r = 15/2

dm/dt = 2 dr/dt -------> 4 = 2 dr/dt -------> dr/dt = 2

As you know the volume of spherical = 4/3 Πr^3

v = 4/3 Π r^3

dv/dt = 4/3 *3 *Π *r^2 dr/dt

dv/dt = 4 Π r^2 * 2

dv/dt = 4 Π(15/2)^2 * 2 = 450Π

I hope it is useful,

Minoo