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Question
If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.
Options
True
False
Solution
This statement is False.
Explanation:
Let the radius of a right circular cone be r and height of a right circular cone be h.
Then, the volume of a right circular cone = `1/3 pir^2 h`
Now, `r = r/2, h = 2h`
New volume of a right circular cone = `1/3 pi(r/2)^2 xx (2h)`
= `1/3 pi xx r^2/4 xx 2h`
= `1/3 pi xx r^2/2 h`
= `1/2(1/3 pir^2 h)`
Hence, the new volume of a right circular cone becomes half of original volume of a right circular cone.
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