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

Question

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 heightof 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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