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Q.

The slant height of a right circular cone is halved, keeping the height same, then the ratio of the volume of the reduced cone to that of the original cone is

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a

\frac{l^{2} + 4 h^{2}}{4 (l^{2} + h^{2})}

b

\frac{l^{2} + 4 h^{2}}{4 (l^{2} - h^{2})}

c

\frac{l^{2} - 4 h^{2}}{4 (l^{2} + h^{2})}

d

\frac{l^{2} - 4 h^{2}}{4 (l^{2} - h^{2})}

answer is A.

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Detailed Solution

\frac{V^{1}}{V} = \frac{\frac{1}{3} π {(\sqrt{{(\frac{l}{2})}^{2} - h^{2}})}^{2} \times h}{\frac{1}{3} π {(\sqrt{l^{2} - h^{2}})}^{2} \times h}

$= \frac{{(\frac{l}{2})}^{2} - h^{2}}{l^{2} - h^{2}}$

$= \frac{l^{2} - 4 h^{2}}{4 (l^{2} - h^{2})}$

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The slant height of a right circular cone is halved, keeping the height same, then the ratio of the volume of the reduced cone to that of the original cone is