The measurement of the edge of a cube is found to be 18 inches,with a possible error of 0.7 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) 816.48, 151.20
B) 544.32, 136.08
C) 612.36, 136.08
D) 544.32, 120.96
E) 680.40,151.20

Question

​The measurement of the edge of a cube is found to be 18 inches,with a possible error of 0.7 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) ​816.48, 151.20
B) ​544.32, 136.08
C) ​612.36, 136.08
D) ​544.32, 120.96
E) ​680.40,151.20

Quizplus · Accepted Answer

We use the formulas for the volume and surface area of a cube to estimate the propagated error:

(a) Volume of cube = (edge length)^3
Taking the differential of both sides:
dV = 3(edge length)^2 * d(edge length)
Estimating the propagated error:
dV = 3(18)^2 * 0.7 = 680.4 in^3

(b) Surface area of cube = 6(edge length)^2
Taking the differential of both sides:
dA = 12(edge length) * d(edge length)
Estimating the propagated error:
dA = 12(18) * 0.7 = 151.2 in^2

Therefore, the answer is E.

​The Measurement of the Edge of a Cube Is Found

The Measurement of the Edge of a Cube Is Found