Maxima or minima?

**sanikui** · March 24th 2009, 01:08 AM

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.

**CaptainBlack** · March 24th 2009, 02:57 AM

Originally Posted by sanikui

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.

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

**u2_wa** · March 24th 2009, 03:14 AM

Originally Posted by sanikui

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= $h=\sqrt{4^2-r^2}+4$ (see diagram)
$r^2=4^2-(h-4)^2$

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

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

calculate $\frac{dV}{dh}=0<br />$

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

Put this value of h in equation $V=\frac{1}{3}\pi.(4^2-(h-4)^2).h<br />$ to get an answer.

Hope this helps

**sanikui** · March 24th 2009, 03:20 AM

Answer is 79.43cm^3
V^^
Thanks.

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