Question

A spherical balloon is inflated with gas at the rate of  800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters?

Answer 1

Step 1:

The volume of spherical balloon is .

Apply derivative on each side with respect to time .

A spherical balloon is inflated with gas at the rate cm³/min.

The speed of balloon  changes with radius is .

Step 2:

(a) To find how fast is the radius of the balloon increasing at the instant the radius cm.

Substitute cm and cm³/min. in above expression.

cm/min.

Step 3:

(b) To find how fast is the radius of the balloon increasing at the instant the radius cm.

Substitute cm and cm³/min in above expression.

cm/min.

Solution:

(a) The speed of balloon  changes with radius cm is cm/min.

(b) The speed of balloon  changes with radius cm is cm/min.