| If the radius of a cone is doubled, then the volume of the new cone becomes how many times the volume of the original cone? |
A) 4
B) 2
C) 8
D) 6
Correct Answer: A
Solution :
| Let the original radius \[=r\] and original height \[=h\] |
| Original volume \[=\frac{1}{3}\pi {{r}^{2}}h\] |
| New radius \[=2\,r\]and height \[=h\] |
| New volume \[=\frac{1}{3}\times \pi \times {{(2r)}^{2}}\times h=\frac{4}{3}\pi {{r}^{2}}h\] |
| \[=4\times \frac{1}{3}\pi {{r}^{2}}h=4\times \text{Original}\,\,\text{volume}.\] |
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