Question

Three solid metallic spheres of radii $6$, $8$ and $10$ centimetres are melted to form a single solid sphere. The radius of the sphere so formed is __________.

• A. $24$cm
• B. $16$cm
• C. $18$cm
• D. $12$cm

Answer 1

The correct option is D $12$cm

Given are three metallic spheres of radius $6,8,10$ cm.

They are melted to form a single solid sphere.

Now,

Volume of the single solid sphere=Volume of the three spheres

Say the radius of the resulting sphere is $r$ cm.

$\therefore \frac{4}{3}\pi r^3=\frac{4}{3}\pi {\left(6\right)}^3+\frac{4}{3}\pi {\left(8\right)}^3+\frac{4}{3}\pi {\left(10\right)}^3=>r^3=6^3+8^3+{10}^3$

$=>r={\left(1728\right)}^{\frac{1}{3}}=12$cm