# Math Help - Maxima or minima?

1. ## Maxima or minima?

Find the volume of the largest circular cone tat can be cut from a solid sphere of radius 4cm.

Thx.

2. Originally Posted by sanikui
Find the volume of the largest circular cone tat can be cut from a solid sphere of radius 4cm.

Thx.
First thing to do is draw a labled diagram of a cone in the sphere.

Now write the volume of the cone in terms of what you know and any free variables that you had to introduce when you labled the diagram.

CB

3. Originally Posted by sanikui
Find the volume of the largest circular cone tat can be cut from a solid sphere of radius 4cm.

Thx.

I have attached a diagram to illustrate the answer.

Let r be the radius of cone.
height of cone= $h=\sqrt{4^2-r^2}+4$ (see diagram)
$r^2=4^2-(h-4)^2$

Volume of cone $=\frac{1}{3}\pi.r^2.h
$

$V=\frac{1}{3}\pi.(4^2-(h-4)^2).h$

calculate $\frac{dV}{dh}=0
$

I got $h=\frac{16}{3}$cm

Put this value of h in equation $V=\frac{1}{3}\pi.(4^2-(h-4)^2).h
$