If the height and the radius of the base of a cone are both doubled, the volume of the cone becomes _______ of its previous volume.

8 times

Let the height and the radius of the cone = 1 and 1 respectively.

Then the volume of the cone = \(\frac{1}{3}\)πR²H  = \(\frac{1}{3}\)π(1)²(1)  = \(\frac{1}{3}\)π

If the height and the volume of the cone are doubled then the new volume = \(\frac{1}{3}\)π(2)²(2) = \(\frac{1}{3}\)π8

It will become 8 times to the previous volume.