Question

The radii of the bases of a cylinder and a cone are in the ratio 3 : 5 & their heights are in the ratio 3 : 4. What is the ratio of their volumes

Answer 1

$\sf\large{Given:}$

• $\sf\red{The\:ratio\:of\: their\: radius=3:5}$
• $\sf{The\: radius\:of\: cyclinder=3}$
• $\sf{The\: radius\:of\: cone=5}$
• $\sf\red{The\:ratio\:of\: their\: height=3:4}$
• $\sf{The\: height\:of\: cyclinder=3}$
• $\sf{The\: height\:of\:cone=4}$

$\sf\large{To\: Find:}$

• $\sf{The\:ratio\:of\: their\: Volume}$

$\sf\large{Solution:}$

$\sf{\implies Formula\: used}$

$\sf{\implies Volume\:of\:cone=\dfrac{1}{3}\pi\:r^2\:h}$

$\sf{\implies Volume\:of\: cyclinder=\pi\:r^2\:h}$

$\sf{\implies Calculation\:for\: cyclinder}$

$\sf{\implies Volume=\pi*3^2*3}$

$\sf{\implies Volume=\pi*9*3}$

$\sf{\implies Calculation\:for\:cone}$

$\sf{\implies Volume=\dfrac{1}{3}\pi*5^2*4}$

$\sf{\implies Volume=\dfrac{1}{3}\pi*25*4}$

Hence,

$\sf{\implies Ratio=volume\: cyclinder: volume\:cone}$

$\sf{\implies Ratio=\pi*9*3:\dfrac{1}{3}\pi*25*4}$

$\sf{\implies Ratio=9*3*3:25*4}$

$\sf{\implies Ratio=81:100}$

$\sf\purple{\therefore\:The\: ratio\:of\: volume\:of\: cyclinder\:and\:cone=81:100}$

Answer 2

The radii of the bases of a cylinder and a cone are in the ratio 3 : 5 & their heights are in the ratio 3 : 4. What is the ratio of their volumes

By find we get

The ratio of volume of cylinder and cone=81:100

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