The measurement of the edge of a cube is found to be 8 inches, with a possible error of 0.08 inch. Use differentials to estimate the propagated error in computing (a) the volume of the cube and (b) the surface area of the cube. Give your answers to two decimal places.
A)18.43, 7.68
B)12.29, 6.91
C)13.82, 6.91
D)12.29, 6.14
E)15.36, 7.68

Question

Quizplus · Accepted Answer

The volume of a cube is given by $V = s^3$, where $s$ is the side length. The differential $dV$ gives the error in the volume, which can be found using the derivative: $dV = 3s^2 \cdot ds$. Substituting $s = 8$ inches and $ds = 0.08$ inches, we get $dV = 3(8)^2(0.08) = 15.36$ cubic inches.The surface area of a cube is given by $A = 6s^2$. The differential $dA$ gives the error in the surface area, which can be found using the derivative: $dA = 12s \cdot ds$. Substituting $s = 8$ inches and $ds = 0.08$ inches, we get $dA = 12(8)(0.08) = 7.68$ square inches.

The Measurement of the Edge of a Cube Is Found