Question

A solid metallic hemisphere of diameter 28 cm is melted and recast into a number of identical solid cones, each of diameter 14 cm and height 8 cm. Find the number of cones so formed.

Answer 1

Solution:-

Diameter of sphere = 28 cm
Then, radius of sphere = $\frac{28}{2}=14cm$
volume of the sphere = $\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 14\times 14\times 14$

Volume of sphere = $11498.66c{m}^{3}Diameterofcone=14cmradiusofcone=7Volumeofthecone=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi 7^2\times 8Volumeofcone=410.3Numberofconesformed=\frac{11498.66}{410.3}=28cones$