Say true or false.

If the radius of a right circular cone is halved and height is doubled, then the volume will remain unchanged.

True

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False

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Solution

The correct option is B False
False.
Given, radius is halved and height is doubled.
Volume of a cone $= \frac{1}{3} π r^{2} h$
Since new volume $= \frac{1}{3} π {(\frac{r}{2})}^{2} . 2 h = \frac{1}{2}$ (Original Volume)
Thus the statement is false.

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Similar questions

If the radius of a right circular cone is halved and height is doubled, then the volume will remain unchanged.

Q. Say true or false.

If the radius of a cylinder is doubled and height is halved, the volume will be doubled.

Question 5

If the height of a cylinder becomes $\frac{1}{4}$ of the original height and the radius is doubled, then which of the following will be true ?
(a) Volume of the cylinder will be doubled
(b) Volume of the cylinder will remain unchanged
(c) Volume of the cylinder will be halved
(d) Volume of the cylinder will be $\frac{1}{4}$ of the original volume

If the height of a cylinder is doubled and radius remains the same, then volume will be

(a) doubled (b) halved

Q. 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.

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Say true or false.If the radius of a right circular cone is halved and height is doubled, then the volume will remain unchanged.

The correct option is B FalseFalse.Given, radius is halved and height is doubled.Volume of a cone =13πr2hSince new volume =13π(r2)2.2h=12 (Original Volume)Thus the statement is false.

Say true or false.

If the radius of a right circular cone is halved and height is doubled, then the volume will remain unchanged.

The correct option is B False
False.
Given, radius is halved and height is doubled.
Volume of a cone $= \frac{1}{3} π r^{2} h$
Since new volume $= \frac{1}{3} π {(\frac{r}{2})}^{2} . 2 h = \frac{1}{2}$ (Original Volume)
Thus the statement is false.