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:

From the given information:

The volume of the sphere is

Suppose the diameter is represented by P.

i.e P = 2r

and r = P/2

∴

Differentiating both sides;

here;

P = 12

dP = 12.5 - 12

dP = 0.5

∴

= 36π

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

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.