Question

the surface area of a cube is increased from 24 square centimeters to 26.016 square centimeters . use differentials to determine:
(1) by approximately how many centimeters does the side length of the cube increase?

(2) by approximately how many cubic centimeters does the volume of the cube increase?

(3) by approximately what percentage does the volume of the cube increased?

Answer 1

surface area = a = 6 x^2
da/dx = 12 x
so if a = 24, x = 2
da = 12 x dx = 12*2 * dx = 24 dx
if da = 2.016
then dx = da/24 = .084 (answer part 1)

volume = v = x^3 = 8 when x = 2
so
dv/dx = 3 x^2
dv = 3 (2^2)(.084) (part b)

100 (dv / v)