Question

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is

पर्याय

• 12 cm

•  24 cm

•  30 cm

• 36 cm

Answer 1

Let r be the radius of single sphere.

Now,

The volume of single sphere = sum of volume of three spheres

${\displaystyle \frac{4}{3}\pi r^3=\frac{4}{3}\pi {\left(61\right)}^3+\frac{4}{3}\pi {\left(8\right)}^3+\frac{4}{3}\pi {\left(10\right)}^3}$

${\displaystyle \frac{4}{3}\pi r^3=\frac{4}{3}\pi (216+512+1000)}$

       ${\displaystyle r^3=1728}$

         ${\displaystyle r=12cm}$

Hence, the diameter = 20 × r = 24 cm