Question

If the radius of a sphere is measured as $8cm$ with a error of $0.03cm$, then the approximate error calculate its volume is

• A. $7.92\pi c{m}^3$
• B. $7.68\pi c{m}^3$
• C. $7.86\pi c{m}^3$
• D. $6.68\pi c{m}^3$

Answer 1

Answer: (C)

$7.86\pi c{m}^3$

The radius of the sphere $=8$ $cm$

Error in radius$=\Delta r$ $=0.03$ $cm$

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

$\Rightarrow V=\frac{4}{3}\pi r^3$

$\Rightarrow \Delta V=\frac{4}{3}\times 3\pi r^2\Delta r$

$\Rightarrow \Delta V$$=4\pi r^2\Delta r$

$\Rightarrow \Delta V$$=4\pi \times 8\times 8\times 0.03$

$\Rightarrow \Delta V$$=7.68\pi$ $c{m}^3$

So, approximate error in its volume is $7.86$ $c{m}^3$