If the base radius of a cone is doubled and its height is halved, then the volume of the new cone will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 times that of the original cone
The volume of a cone is \(\frac{1}{3}\pi r^{2}h\): it grows with the square of the radius but only in proportion to the height.
Doubling the radius multiplies the volume by \(2^{2}=4\)
Halving the height multiplies it by \(\frac{1}{2}\)
New volume \(\displaystyle =\frac{1}{3}\pi(2r)^{2}\times\frac{h}{2}=2\times\frac{1}{3}\pi r^{2}h\), that is, twice the original