Question

If the height and radius of a cone are doubled, then the volume becomes
A. 2 times
B. 4 times
C. 6 times
D. 8 times

Answer 1

Hint: we know that the volume of a cone with radius r and height h is $\dfrac{1}{3}\pi {r^2}h{\text{ }}cubic{\text{ }}units$and when the radius and height are doubled we get r = 2r and h = 2h and substituting in the volume we will get the required solution.

Complete step by step answer:

Let us consider a cone with radius r and height h
So the volume of the cone = $\dfrac{1}{3}\pi {r^2}h{\text{ }}cubic{\text{ }}units$
Now we are given that the radius and the height is doubled
That is R = 2r and H=2h
And now the volume of the cone = $\dfrac{1}{3}\pi {R^2}H{\text{ }}cubic{\text{ }}units$
                                                            $
   = \dfrac{1}{3}\pi {(2r)^2}(2h) \\
   = \dfrac{1}{3}\pi (4{r^2})(2h) \\
   = \dfrac{8}{3}\pi {r^2}h{\text{ }}cubic{\text{ }}units \\
$
Therefore the new volume = 8 * ( volume of the cone with radius r and height h)
From this, we get that when the radius and height are doubled then the volume becomes 8 times the volume with radius r and height h
Therefore the correct option is D.

Note: Many students tend to say two times or four times as we are given that the radius and height are doubled, which is wrong. Remember that we need to substitute the values in the formula to get the required solution.