Volume and Ratio - Similar Shapes

[janvianish]

Hi,
I was stuck on a question and was wondering if anyone could help me.

A cone is split into two pieces of equal volume. Show that the large cone is about 26% taller than the small cone
Hint: begin by finding the volume scale factor for the two cones

Thanks

 

[DrPhil]

Hi,
I was stuck on a question and was wondering if anyone could help me.

A cone is split into two pieces of equal volume. Show that the large cone is about 26% taller than the small cone
Hint: begin by finding the volume scale factor for the two cones

Thanks

My mental image is that you have a (right circular) cone sitting on a table, and you cut it across with a plane such that half of the volume is in the frustum and half in a (small) cone. Have you considered the Hint? Please show us your work.