Question

A cone is cut into two parts from the midpoint of the axis.find the ratio of volume of the small cone to the original cone

Answer 1

Volume of original cone = πr²h/3

When the cone is cut into half:
H = h/2
H/R = h/r
R = Hr/h = r/2

Volume of smaller come :
V = πR²H/3
V = π(r/2)²(h/2)/3
V = πr²h/24

ratio= volume of small cone/volume of original​ cone
ratio = (πr²h/24)/(πr²h/3)
= 1/8

ratio= 1:8

i hope you understand the approach.
All the best.