Consider a rectangular solid with a square end of side length 10 inches and a length of 20 inches. If the measurements are accurate to within 0.1 inch, then the estimated error of the volume in cubic inches using differential is

A)50
B)72.5
C)88.1
D)93.7
E)102.3

Question

Consider a rectangular solid with a square end of side length 10 inches and a length of 20 inches. If the measurements are accurate to within 0.1 inch, then the estimated error of the volume in cubic inches using differential is
​
A)50
B)72.5
C)88.1
D)93.7
E)102.3

Quizplus · Accepted Answer

The volume V of the rectangular solid is given by V = s^2 * l, where s is the side length of the square end and l is the length. Using differentials, dV = 2sl * ds + s^2 * dl. Substituting s = 10, l = 20, ds = 0.1, and dl = 0.1, we get dV = 2(10)(20)(0.1) + (10)^2(0.1) = 40 + 10 = 50 cubic inches.

Consider a Rectangular Solid with a Square End of Side