A hot air balloon is being inflated by 2 cubic ft of air per second. How fast is the radius increasing after 1 minute?

Question

A hot air balloon is being inflated by 2 cubic ft of air per second. How fast is the radius increasing after 1 minute?

a. 0.017 ft/sec

b. 0.02 ft/sec

c. 0.03 ft/sec

d. 0.1 ft/sec

e. None of the above.

Answer 1

v= (4/3)pi(r^3)

r= cube root of 3v/4pi

r(60)= (45/pi)^(1/3)

v'= 4pir^2r'= 2

v=2t

v(60)= 120

r' = 1/2pir^2

r'(60)= 1/2(45/pi)^(2/3)

= about 1/2(45/3.141593)^(2/3)

= about 0.085

= about 0.1 feet per second