Question

. If the ratio of radii of two spheres is 4:7, find the ratio of their volumes.​

Answer 1

Step-by-step explanation:

Given ratio of radii of two spheres is 4 : 7

We know that,

Volume of a sphere with radii r is

\frac{4}{3} \pi {r}^{3}

3

4

πr

3

Ratio of Volume of the given spheres =

\begin{gathered} \frac{4}{3} \pi( {4}^{3} ) \div \frac{4}{3} \pi( {7}^{3} ) \\ \\ = {4}^{3} \div ( {7}^{3} ) \\ \\ = \frac{64}{343} \end{gathered}

3

4

π(4

3

)÷

3

4

π(7

3

)

=4

3

÷(7

3

)

=

343

64

Therefore, Ratio of their volumes is 64 : 343 .

Answer 2

Answer :

64 : 343

Explanation :

Ratio of radii of two spheres is 4 : 7

Let's assume,

Radius of one sphere = $4x$

Radius of another sphere = $7x$

We know that,

Volume of a cylinder : $\to \sf \dfrac{4}{3} \pi \boldsymbol{r}^{3}$

∴ Volume of one sphere :

$\to \sf \dfrac{4}{3}\pi (4\boldsymbol{x)}^{3}$

$\to \sf \dfrac{256\boldsymbol{x}^{3}}{3}\pi$

And also,

Volume of another sphere :

$\to \sf \dfrac{4}{3}\pi \boldsymbol{r}^{3}$

$\to \sf \dfrac{4}{3} \pi (7\boldsymbol{x)}^{3}$

$\to \sf \dfrac{1372\boldsymbol{x}^3}{3}\pi$

Forming in ratio :

$\to \sf V_1 : V_2$

$\to \sf \dfrac{256\boldsymbol{x}^{3}}{3}\pi : \dfrac{1372\boldsymbol{x}^{3}}{3}\pi$

$\to \sf 64 : 343$