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A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute.

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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?
asked Jan 22, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The volume of spherical balloon is image.

Apply derivative on each side with respect to time image.

image

image

image

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

The speed of balloon  changes with radius is image.

Step 2:

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

image

Substitute image cm and image cm3/min. in above expression.

image

image

image

image cm/min.

Step 3:

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

image

Substitute image cm and image cm3/min in above expression.

image

image

image

image cm/min.

Solution:

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

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

answered Jan 22, 2015 by Sammi Mentor

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