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Question

  • A cylinder, a cone and a hemisphere are of same base and of same height. Find the ratio of their volumes ?


Solution

We have,
A cylinder $$= A$$ cone $$= A$$ hemisphere $$ = $$ same height
then, we know that
Cylinder volume = $$\pi r^{2} h=V_{1}$$
Cone volume = $$\dfrac {1}{3}\pi r^{2} h=V_{2}$$
Hemisphere volume = $$\dfrac {3}{2}\pi r^{2} h=V_{3}$$
when $$h=$$ height
$$r=$$radius of Base
According to given question,
$$V_{1}: V_{2}: V_{3}=\pi r^{2} h: \dfrac {1}{3}\pi r^{2} h: \dfrac {2}{3}\pi r^{2}$$
$$V_{1}: V_{2}: V_{3}=3:1:2$$
Hence, this is the answer.

Mathematics

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