Question

A spherical party balloon is being inflated with helium pumped in at a rate of 3 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 3 ft?

Answer 1

V=3t=4/3*r^3*pi

Answer 2

speed = flow rate / area => s = Q/A

the area of a circle is A = pi*r^2


when r = 3 ft then A = pi*3^2 = 9*pi
Q = 3 cubic feet per minute


so finally:

s = 3/(9*pi) = 1/(3*pi) feet/minute


Thats how fast it is growing

Answer 3

The problem has to do with volume and surface area
The volume of a sphere of radius r is
V =
4/3πr3.
Round your answer to two decimal places.