# THREE SOLID SPHERES OF IRON HAVING DIAMETER 2CM , 12CM AND 16CM RESPECTIVELY ARE MELTED INTO SPHERE.FIND THE RADIUS OF THE NEW SPHEREi 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 r1, r2, r3 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
$⇒\frac{4}{3}{{\mathrm{\pi r}}_{1}}^{3}+\frac{4}{3}{{\mathrm{\pi r}}_{2}}^{3}+\frac{4}{3}{{\mathrm{\pi r}}_{3}}^{3}=\frac{4}{3}{\mathrm{\pi R}}^{3}\phantom{\rule{0ex}{0ex}}⇒{{\mathrm{r}}_{1}}^{3}+{{\mathrm{r}}_{2}}^{3}+{{\mathrm{r}}_{3}}^{3}={\mathrm{R}}^{3}\phantom{\rule{0ex}{0ex}}⇒\left(1{\right)}^{3}+\left(6{\right)}^{3}+\left(8{\right)}^{3}={\mathrm{R}}^{3}\phantom{\rule{0ex}{0ex}}⇒{\mathrm{R}}^{3}=729\phantom{\rule{0ex}{0ex}}⇒\mathrm{R}=9$
Thus, the radius of new sphere=9 cm

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