Question

Three solid spheres of a lead are melted into a single solid sphere If the radii of the three spheres be 1 cm, 6 cm and 8 cm respectively Then radius of the new sphere is :

• A. $2cm$
• B. $3cm$
• C. $5cm$
• D. $9cm$

Answer 1

The correct option is D $9cm$

Let r be the radius of the new sphere Then
$\frac{4}{3}\pi r^3=\frac{4}{3}\pi {\left(1\right)}^3+\frac{4}{3}\pi {\left(6\right)}^3+\frac{4}{3}\pi {\left(8\right)}^3$
$\frac{4}{3}\pi [{\left(1\right)}^3+{\left(6\right)}^3+{\left(8\right)}^3]=\frac{4}{3}\pi [1+216+512]$
or $r^3=729={\left(9\right)}^3$
$\therefore$ Radius of the new sphere (r) =9 cm