Choose the correct answer of the following question:

Question:

Choose the correct answer of the following question:

If the radius of a sphere becomes 3 times, then its volume will become

(a) 3 times                         (b) 6 times                         (c) 9 times                         (d) 27 times   

Solution:

Let the radius of the given sphere and that of the new sphere be $r$ and $R$, respectively;

Also, the volume of the given sphere and that of the new sphere be $v$ and $V$, respectively.

We have,

$R=3 r \quad \ldots \ldots(\mathrm{i})$

Now,

$\frac{\text { Volume of the new sphere }}{\text { Volume of the given sphere }}=\frac{\left(\frac{4}{3} \pi \mathrm{R}^{3}\right)}{\left(\frac{4}{3} \pi \mathrm{r}^{3}\right)}$

$=\left(\frac{R}{r}\right)^{3}$

$=\left(\frac{3 r}{r}\right)^{3} \quad[\operatorname{Using}(\mathrm{i})]$

$=3^{3}$

$=27$

Hence, the correct answer is option (d).

 

 

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