Quantitative Aptitude Ques 220

Question: If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be

Options:

A) 3 : 8

B) 8 : 3

C) 3 : 4

D) 4 : 3

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ V _1,:,{V _{2,}},=,2,:,3 $ $ r _1:r _2=1:2, $ $ h _1:h _2=? $ Now, $ \frac{v _1}{v _2}=\frac{2}{3}\Rightarrow \frac{\frac{1}{3}\pi r_1^{2}h _1}{\frac{1}{3}\pi r_2^{2}h _2}=\frac{2}{3} $

$ \Rightarrow $ $ {{( \frac{r _1}{r _2} )}^{2}}\times \frac{h _1}{h _2}=\frac{2}{3} $

$ \Rightarrow $ $ \frac{1}{4}\times \frac{h _1}{h _2}=\frac{2}{3} $

$ \Rightarrow $ $ \frac{h _1}{h _2}=\frac{8}{3} $

$ \therefore $ $ h _1:h _2=8:3 $

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