A circular piece of card with a sector removed is folded to form a conte. The slanted height of the cone is 12cm and the vertical height is h.
Show that the volume of the cone ${Vcm^2}$ is given by the expression
${V = {1\over 3}\pi h(144 – h^2)}$
The volume of a cone is ${{1\over 3}\pi r^2h}$
${3 = \pi r^2h}$
${h = {3\over {\pi r^2}}}$
I would then plug h into the original volume equation:
${{1\over 3}\pi r^2{3\over {\pi r^2}}}$
Which is obviously far removed from the original question.
I don't get where the equation in the question comes from
Best Answer
Hint:
the slanted height ($12$) is the hypotenuse of a rectangular triangle that has, as other sides, the height ($h$) and the radius ($r$) of the basis of the cone. So $144-h^2=r^2$