How many times will the volume of the cone decrease if its height is reduced by 9 times

How many times will the volume of the cone decrease if its height is reduced by 9 times, and the radius of the base remains the same?

Initial cone volume V1:

V1 = (Sbase * h1) / 3 (Sbase – base area, h1 – height)

The volume of the cone V2 after decreasing the height by a factor of 9:

h2 = h1 / 9;

V2 = (Ssn. * H2) / 3 = (Ssn. * (H1 / 9)) / 3.

Volume ratio:

V1 / V2 = ((Ssn. * H1) / 3) / (Ssn. * (H1 / 9)) / 3 = 9.

V1 = 9V2.

Answer. The volume of the cone will decrease 9 times.