Question

27 small spheres with radius 5cm are melted to form a new sphere. Find the radius of the new sphere.

Answer 1

Given radius of small spheres = 5 cm
$\therefore Volume=\frac{4}{3}\pi r^3$
volume of 27 small spheres = $27\times \frac{4}{3}\pi r^3=36\pi r^3$
Let R be the radius of big sphere
$\therefore$ Volume of 27 small sphers = Volume of big sphere
$\Rightarrow 36\text{/}\pi r^3=\frac{4}{3}\text{/}\pi R^3\Rightarrow \frac{36\times 3}{4}\times r^3=R^3\Rightarrow R^3=27\times (5{)}^3\Rightarrow R^3=3^3\times 5^3\Rightarrow R=3\times 5=15cm$