Question

If there is an error of $m$% in measuring the edge of cube, then the present error in estimating its surface area is

• A. $2m$
• B. $3m$
• C. $1m$
• D. $4m$

Answer 1

Answer: (A)

$2m$

Surface area $A$ of a cube of side $x$ is given by $A=6x^2$
On differentiating w.r.t. $x$, we get
$\frac{dA}{dx}=12x$
Let the change in $x$ be $△x=m$% of $x=\frac{mx}{100}$
Change in surface area,
$△A=\left(\frac{dA}{dx}\right)△x=\left(12x\right)△x$
$=12x\left(\frac{mx}{100}\right)=\frac{12x^{2}m}{100}$
$\therefore$ The approximate change in surface area
$=\frac{2m}{100}\times 6x^2$
$=2m$% of original surface area.

Hence, the answer is $2m$.