The edge of a cube was found to be 30 cm with a possible error in measurement of .1 cm

Question

The edge of a cube was found to be 30 cm with a possible error in measurement of .1 cm. Use differentials to estimate the percentage error (to the nearest hundredth) in computing (a) the volume of the cube and (b) the surface area of the cube.

Answer 1

Well the edge is 30 cm +- 0.1 cm

Volume will be side cubed, so max estimate for volume is (30.1)^3, and minimum (29.9)^3

So percentage error = [(30.1)^3 - 30^3/ / 30^3 x 100 = 1,00 %

Surface area is 6 x side squared

So max estimate for area is 6 x 30.1^2, minimum 6 x 29.9 ^ 2

So percentage error = (6 x 30.1^2 - 6 x 30^2) / (6 x 30^2) x 100 = 0.67 %