The radius of a spherical balloon is measured to be 9 inches,with a possible error of 0.02 inch.Use differentials to approximate the maximum possible error in calculating the volume of the sphere.Round your answer to two decimal places.
A)±10.18 cubic inches
B)±5.65 cubic inches
C)±30.54 cubic inches
D)±20.36 cubic inches
E)±4.52 cubic inches

Question

The radius of a spherical balloon is measured to be 9 inches,with a possible error of 0.02 inch.Use differentials to approximate the maximum possible error in calculating the volume of the sphere.Round your answer to two decimal places. ​
A)±10.18 cubic inches
B)±5.65 cubic inches
C)±30.54 cubic inches
D)±20.36 cubic inches
E)±4.52 cubic inches

Quizplus · Accepted Answer

The formula for the volume of a sphere is V = (4/3)πr^3. 
Taking the differential of this formula, we get dV = 4πr^2 dr.

Plugging in r = 9 and dr = 0.02, we get:
dV = 4π(9)^2 (0.02) = 40.68

Therefore, the maximum possible error in calculating the volume of the sphere is approximately ±20.34 cubic inches, which rounds to ±20.36 cubic inches. 
The best choice is D.

The Radius of a Spherical Balloon Is Measured to Be