Question

The radius of a cone decreased to one-third and its volume remains same .then the new length is how many times the original length ?

Answer 1

Answer:

Let radius = r

Volume = $\tt{\frac{\pi r^{2} h}{3}}$

New radius = r/3

Volume = $\tt{\frac{\pi r'^{2} h'}{3}}$

Volume remains same, thus:

=> $\tt{\frac{\pi r^{2} h}{3} = \frac{\pi r'^{2} h'}{3}}$

=> h' = 9h

Thus, the length becomes 9 times the original length

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