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Maths-

General

Easy

Question

A Cylinder and cone are of the same height. If diameter of their bases are in the ratio 2:3, Find the ratio of their volumes?

hint Hint:

We take the common ratio as 1 and proceed further with the formulae to find the ratio.

The correct answer is: The ratio of their volumes is Cylinder : Cone = 4:3

Explanations:
Step 1 of 2:
Let the common ratio be 1.
Then the diameter of the bases of cylinder and cone be 2 and 3. The respective radii are 1 and 3/2.
We know that
Volume of cylinder = $pi r squared h equals pi left parenthesis 1 right parenthesis squared h$
Volume of cone = $1 third pi r squared h equals 1 third pi open parentheses 3 over 2 close parentheses squared h$
Since is same for both
Step 2 of 2:
So, the ratio of their volumes = cylinder : cone
$equals fraction numerator pi left parenthesis 1 right parenthesis squared h over denominator 1 third pi open parentheses 3 over 2 close parentheses squared h end fraction$
$equals fraction numerator 1 squared over denominator 1 third cross times 9 over 4 end fraction comma pi text and end text h text get cancelled out end text$
$equals 3 cross times 4 over 9$
$equals 4 over 3 equals 4 colon 3$
Final Answer:
The ratio of their volumes is Cylinder : Cone = 4:3

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