Question

Question 2
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Answer 1

Radii of spheres = 6 cm, 8 cm, 10 cm
Volume of sphere
$=\frac{4}{3}\pi r^3$
Total volume of three spheres

$=\left(\frac{4}{3}\pi 6^3\right)+\left(\frac{4}{3}\pi 8^3\right)+\left(\frac{4}{3}\pi {10}^3\right)$
$=\frac{4}{3}\pi (6^3+8^3+{10}^3)$
$=\frac{4}{3}\pi (216+512+1000)$
$=\frac{4}{3}\pi \times 1728$
let the radius of big sphere be R
Volume of big sphere = Total volume of three spheres
$=\frac{4}{3}\pi R^3$= $=\frac{4}{3}\pi \times 1728$
Hence radius of biggest sphere
$R=\sqrt[3]{31728}=12cm$