Question

The radius of a sphere is measured as $14cm$. Later it was found that there is an error $0.02cm$ in measuring the radius. Find the approximate error in surface area of the sphere.

Answer 1

Radius of the sphere $=14m$

Error in measurement of radius = $△r=0.02m$

Volume of the sphere $V=\frac{4}{3}\pi r^3$

$△V=\frac{dV}{dr}△r$ ___ (1)

$\frac{dV}{dx}=\frac{4}{3}\times 3r^2\times \pi △r$ (Diff with respect to x)

substitute the value of $\frac{dv}{dx}$ and $△r$ in eq (1)

$△v=\frac{4}{3}\times 3r^2\times \pi \times 0.02$

$=4\pi r^2\times 0.02=4\pi {14}^2\times 0.02$

$=784\pi \times 0.02$

$=15.68\pi m^3$