Question

How many cones of 3$cm$ radius and 6$cm$ height are formed by melting a metallic sphere of radius 9$cm.$

Answer 1

Volume of sphere$=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times 9^3=4\times 9\times 9\times 3=972\pi c{m}^3$

Volume of one cone$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \times 3^2\times 6=3\times 6=18\pi c{m}^3$

Number of cones$=\frac{\text{Volume of sphere}}{\text{Volume of cone}}=\frac{972\pi }{18\pi }=54$

Number of cones$=54$