Question:
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is
(a) 12 cm
(b) 24 cm
(c) 30 cm
(d) 36 cm
Solution:
Let r be the radius of single sphere.
Now,
The volume of single sphere = sum of volume of three spheres
$\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi(61)^{3}+\frac{4}{3} \pi(8)^{3}+\frac{4}{3} \pi(10)^{3}$
$r^{3}=1728$
$r=12 \mathrm{~cm}$
Hence, the diameter = 20 × r = 24 cm
Hence, the correct answer is choice (b).