Question

The radius of a sphere is $5$ cm. Its volume will be given by (according to the theory of significant figures) :

• A. $523.33{cm}^3$
• B. $5.23{\times {10}^{2}cm}^3$
• C. $5.0{\times {10}^{2}cm}^3$
• D. $5{\times {10}^{2}cm}^3$

Answer 1

Answer: (D)

$5{\times {10}^{2}cm}^3$

Volume$=\frac{4}{3}{\pi r}^3=\frac{4}{3}\times \pi {\left(5\right)}^3=523.33{cm}^3$$=5.2333\times {10}^{2}c{m}^3$
$\downarrow$
5 significant figures
Since radius has single significant figure, so, volume should also have single significant figure.

For single significant figure, we have to drop all after decimal.
$\Rightarrow$ Volume $=5\times {10}^{2}c{m}^2$ (if the digit to be dropped is less than 5, preceding digit is left unchanged)