A beach ball is inflated so its diameter increases from 12 inches to 12.5 inches. Given that the formula for the volume of a sphere is V=4/3π,r^3 the change in the volume of the beach ball using differentials is approximately. a. 367π cubic inches.
b. 727π cubic inches.
c. 1447π cubic inches.
d. 288.7π cubic inches.

V = 36π cubic inches.

Step-by-step explanation:

Given that:

The volume of the sphere is

If the diameter is represented by P.

Then P = 2r

and r = P/2

∴

By differentiating both sides;

where;

P = 12

dP = 12.5 - 12

dP = 0.5

Then;

= 36π

Thus, the volume is V = 36π cubic inches.

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step-by-step explanation:

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