Question

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter `"4"2/3` cm and height 3 cm. Find the number of cones so formed.

Answer 1

We have, 

Radius of the metallic sphere, R `= 28/2 = 14   "cm"`

Radius of the smaller cone, t `= "r" =1/2xx("4"2/3)=1/2xx14/3xx7/3 "cm"`

Now,

The number of cones so formed `= "Volume of the metallic sphere"/"Volume of a smaller cone"`   

`=((4/3pi"R"^3))/((1/3pi"r"^2"h"))`

`="4R"^3/("r"^2"h")`

`=(4xx14xx14xx14)/(7/3xx7/3xx3)`

= 672

So, the number of cones so formed is 672.

Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.