A conical dome of a palace is supported by a cylindrical pillar, both having t

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A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of the height of the pillar to that of dome is 4:3, then what is the ratio of their volumes?

Options:

A . 2:1

B . 3:1

C . 4:1

D . 1:1

Answer: Option C
:
C

Given that, the ratio of the height of the pillar to that of dome is 4:3 .
$\Rightarrow \frac{h_{c y l i n d e r}}{h_{c o n e}} = \frac{4}{3}$
We know that,
$v o l u m e o f c y l i n d e r = π r^{2} h$ .
$v o l u m e o f c o n e = \frac{1}{3} π r^{2} h$ .
Now, ratio of volume of cylinder to the volume of cone
$= \frac{π r^{2} h_{c y l i n d e r}}{\frac{1}{3} π r^{2} h_{c o n e}}$
$= \frac{π r^{2} \times 4}{\frac{1}{3} π r^{2} \times 3}$
$= \frac{4}{1}$
$= 4 : 1$

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