# THREE SOLID SPHERES OF IRON HAVING DIAMETER 2CM , 12CM AND 16CM RESPECTIVELY ARE MELTED INTO SPHERE.FIND THE RADIUS OF THE NEW SPHERE

i have read the answer to this question but in the question says the diameters are 2cm. 12cm and 16cm. so the radius will be 1cm, 6cm, 16cm respectively. but when i checked the older answer the radius was taken as 2cm, 12cm, 16cm

Given: Radii *r*_{1}, *r*_{2},* **r*_{3} of three spheres are 1 cm, 6 cm and 8 cm.

Let radius of new sphere be *R.*

As, we know that,

Also,as three spheres are melted into a single sphere.

∴ Sum of volumes of three spheres = Volume of new sphere

$\Rightarrow \frac{4}{3}{{\mathrm{\pi r}}_{1}}^{3}+\frac{4}{3}{{\mathrm{\pi r}}_{2}}^{3}+\frac{4}{3}{{\mathrm{\pi r}}_{3}}^{3}=\frac{4}{3}{\mathrm{\pi R}}^{3}\phantom{\rule{0ex}{0ex}}\Rightarrow {{\mathrm{r}}_{1}}^{3}+{{\mathrm{r}}_{2}}^{3}+{{\mathrm{r}}_{3}}^{3}={\mathrm{R}}^{3}\phantom{\rule{0ex}{0ex}}\Rightarrow (1{)}^{3}+(6{)}^{3}+(8{)}^{3}={\mathrm{R}}^{3}\phantom{\rule{0ex}{0ex}}\Rightarrow {\mathrm{R}}^{3}=729\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{R}=9$

Thus, the radius of new sphere=9 cm

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