The volume of a cube is increased from 729 cubic centimetres to 849.285 cubic centimetres

Question

Use differentials to determine :

(a) by approximately how many centimetres does the side length of the cube increase?
(b)by approximately how many centimetres does the surface area of the cube increase?
(c) by approximately what percentage does the surface area of the cube increase?

Answer 1

Hint:
http://www.jiskha.com/display.cgi?id=1413053733

Answer 2

v = x^3
729 = 9^3 so x = 9
dv = 3 x^2 dx = 243 dx = 849.285 - 729
etc

Answer 3

Use differentials to determine by approximately what percentage does the perimeter of a square table increase if its diagonal is increased from 30 centimetres to 31.245 centimetres