volume AND ration - similar shapes

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 http://www.freemathhelp.com/forum/im...icon_smile.gif

Re: volume AND ration - similar shapes

Remember that the volume of a cone is equal to 1/3 base area times height. If the height of the taller cone is a factor x times larger than the smaller cone, then the radius of the base of the larger cone is that same factor x times larger as well, because the two cones are similar. This means the area of the base of the larger cone is times larger than the area of the base of the smaller cone - do you see whythat is? Consequently the volume of the larger cone is a factor times bigger than the volume of the smaller cone. From this - can you determine what the value of x must be be for the larger cone to be twice the volume of the smaller cone?

Re: volume AND ration - similar shapes

thks..i need to understand it more i think...