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 $\displaystyle x^2$ 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 $\displaystyle x^3$ 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...