Physics

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


ANSWER

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


SOLUTION
Volume$$=\dfrac{4}{3}{\pi r}^{3}=\dfrac{4}{3}\times \pi \left ( 5 \right )^{3}=523.33\ {cm}^{3}$$$$=5.2333\times 10^{2}\ cm^{3}$$
                                                                                   $$\downarrow $$
                                                                          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 $$= 5\times 10^{2}\ cm^{2}$$ (if the digit to be dropped is less than 5, preceding digit is left unchanged)
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