Question

A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base Find the ratio of the volumes of two parts

Answer 1

`AD=12/2=6 cm =h/2`
`tantheta=r/h=(DE)/(h/2)`
`DE=r/2`
Volume of cone AEF=`1/3*pi(r/2)^2(h/2)`
`=1/3pir^2h/8`
Volume of cone=`1/3*pir^2h`
Volume of `2^(nd)` part=`1/3pir^2h-1/3pir^2h/8`
`=7/8pir^2h/3`
`V_1/V_2=(1/3pir^2h/8)/(7/8pir^2h/3)=1/7`.