The side of the cube is x m and side of the cube decrease by 1%.
Let, Δx denotes change in x.
Surface area of any cube is given by,
S=6 x 2
Now,
Δx= 1 100 x =0.01x
So, the change in the surface area,
dS= dS dx Δx
By substituting the given values in the above expression, we get.
dS= d( 6 x 2 ) dx ×Δx =6×2x×( 0.01x ) =0.12 x 2 m 2
Thus, the change in surface area of cube of side x mwhen side is decreased by 1% is 0.12 x 2 m 2 .
Find the approximate change in the surface area of a cube of side x metre caused by decreasing the side by 1%.
Find the approximate change in total surface area of a cube of side x metre caused by increase in side by 1%.