Question 22
Three spheres of radii 3 cm, 4 cm and 5 cm are melted to form a new sphere. Then, the radius of the new sphere is
Solution
If the three spheres are melted to form the larger sphere, then the sum of the volumes of smaller spheres is equal to the volume of the larger sphere.
Let us assume the radius of the larger sphere = R.
$$\frac{4}{3}\pi\ R^3=\frac{4}{3}\pi\ 3^3+\frac{4}{3}\pi4^3+\frac{4}{3}\pi5^3\ $$
This gives : $$R^3=3^3+4^3+5^3=216$$
R = 6 cm.
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