Processing math: 100%
 
+0  
 
+2
602
1
avatar+136 

A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 8. What are the dimensions of such a cylinder which has maximum volume?

Radius =  

Height = 

 May 3, 2022
 #1
avatar+9675 
+1

Suppose r is the base radius of the cylinder inscribing the cone. Let h be the height.

Using similar triangles on the largest cross-section, 

h8r=6.58h=1321316r

 

Then the volume is πr2h=1316πr2(8r).

Solving ddr1316πr2(8r)=0 gives r = 16/3 or r = 0 (rej.)

 

Note that 

d2dr2|r=1631316πr2(8r)=13π<0. Then maximum volume is attained when r = 16/3.

 

Now, you can calculate the height and get your answer.

 May 3, 2022

1 Online Users