How many solid spheres of radius 3 cm can be made by melting a solid cone of radius 2 cm and height 45 cm?

Q.How many solid spheres of radius 3 cm can be made by melting a solid cone of radius 2 cm and height 45 cm? (a) 5 (b) 12 (c) 14 (d) 7

Answer: A

Volume of the cone \[ = \pi \times 2^2 \times 45 = 180\pi \text{ cubic cm} \] Volume of each solid sphere \[ = \frac{4}{3} \pi \times 3^3 = 36\pi \text{ cubic cm} \] \(\therefore\) Number of spheres \[ = \frac{180\pi}{36\pi} = 5 \]