Two cones have their heights in the ratio 1 3 If the radii of their bases are in the ratio 3 1 then ...........

Quantitative Aptitude (CDS) Mensuration 2D

Two cones have their heights in the ratio 1 : 3. If the radii of their bases are in the ratio 3 : 1, then the ratio of their volumes will be

1:1

2:1

3:1

9:1

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Explanation:

$\small Let \: \frac{h1}{h2}=\frac{1}{3}\: \: =>h1=\frac{h2}{3}$
$and \: \frac{r1}{r2}=\frac{3}{1}\: \: =>r1=3r2$
$\frac{v1}{v2}=\frac{\frac{1}{3}\pi r1^{2}h1}{\frac{1}{3}\pi r2^{2}h2}$
$\frac{v1}{v2}=\frac{r1^{2}h1}{ r2^{2}h2}$
$\frac{v1}{v2}=\frac{3}{1}$