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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.
Solution
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.
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