Use differentials to estimate the percentage error

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.

(a) ___

(b) .67

I have part (b) but have calcualted .10 for part (a) which is not correct. any help thanks!

Answer 1

v = a³; dv = 3a²da. Procent error ε = dv/v = 3da/a = 3·0.1cm/30cm = 0.01 = 1%

s = 6a²; ds = 12ada. Procent error ε = ds/s = 12ada/6a² = 2da/a = 2·0.1cm/30cm = 0.00667 = 0.667%