Find the volume of the largest circular cone tat can be cut from a solid sphere of radius 4cm.
My problem was not sure which equation can be use in this question....please help !
Thx.
I have attached a diagram to illustrate the answer.
Let r be the radius of cone.
height of cone=$\displaystyle h=\sqrt{4^2-r^2}+4$ (see diagram)
$\displaystyle r^2=4^2-(h-4)^2$
Volume of cone$\displaystyle =\frac{1}{3}\pi.r^2.h
$
$\displaystyle V=\frac{1}{3}\pi.(4^2-(h-4)^2).h$
calculate $\displaystyle \frac{dV}{dh}=0
$
I got $\displaystyle h=\frac{16}{3}$cm
Put this value of h in equation $\displaystyle V=\frac{1}{3}\pi.(4^2-(h-4)^2).h
$ to get an answer.
Hope this helps