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 $\"\"$ cm^3/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 $\"\"$ cm^3/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.