Question

2 spheres of same metal weigh 1 kg and 7 kg. The radius of smaller sphere is 3 cm. The 2 spheres are melted to form a big sphere. Find diameter of new sphere.

Answer 1

Weight of two spheres of same metal are 1 kg and 7 kg and radius of smaller sphere = 3 cm
$\Rightarrow$ Volume of smaller sphere $=\frac{4}{3}\pi (3cm{)}^3$
$=\frac{4}{3}\pi 27c{m}^3$
$=4\pi \times 9c{m}^3$
$=36\pi c{m}^3$
Thus 1 kg occupies $36\pi c{m}^3$ space also when both sphere are melted the weight of re-casted sphere is equal to sum of individual weights of sphere
$\Rightarrow$ weight of re-casted sphere = 1 kg + 7 kg = 8 kg
Let the radius of re-casted sphere be r.
Then weight of re-casted sphere occupies volume of re-casted sphere space
$\Rightarrow$ 8 kg occupies $\frac{4}{3}\pi r^{3}space$
$\Rightarrow 8\times 36\pi c{m}^3=\frac{4}{3}\pi r^3$
$\Rightarrow r^3=\frac{8\times 36\times 3}{4}c{m}^3=216c{m}^3\Rightarrow r=6cm$

$\Rightarrow$ d = 2r

$\Rightarrow$ d = 2 $\times 6$

$\therefore$ d = 12 cm

Hence the required diameter of sphere is 12 cm.