Question

Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%

Answer 1

The surface area of a cube (S) of side x is given by S = 6x2

\Rightarrow$$\frac{ds}{dx}=($\frac{ds}{dx}$)∇x

$\Rightarrow$(12x)∇x

$\Rightarrow$(12x)(0.01x) [ as1% of x is 0.01x]

$\Rightarrow$0.12x2

Hence, the approximate change in the surface area of the cube is 0.12x2 m2.