Assertion :If the radius of a cone is halved and volume is not changed, then height remains same. Reason: If the radius of a cone is halved and volume is not changed then height must become four times of the original height.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is D Assertion is incorrect but Reason is correct
Assertion is incorrect and reason is true.
Volume of cone $= \frac{1}{3} \times (π) \times r^{2} \times h$
$\frac{V_{1}}{V_{2}} = \frac{(\frac{1}{3}) π r^{2} h_{1}}{(\frac{1}{3}) π (\frac{r}{2})^{2} h_{2}} = \frac{4 h_{1}}{h_{2}}$
As $V_{1} = V_{2}$
$∴ h_{2} = 4 h_{1}$
Thus, if radius is halved, then height must become $4$ times of the original height.

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