Largest Cylinder Volume in Cuboidal Log: What is the Maximum Possible Volume?

[Amith2006]

Homework Statement

What is the volume of the largest cylinder that can be cut out of a cuboidal log of
wood of dimensions 30*20*10 inches?

Homework Equations

volume of cuboid = length*breadth*height
volume of cylinder= *[radius]²*height

The Attempt at a Solution

Radius of largest cylinder=5 inches
height of largest cylinder=30 inches
volume of largest cylinder=750 inch³
But book answer is 1000.

 

[tiny-tim]

Hi Amith2006!

volume of cylinder= *[radius]²*height

Yes, the radius is squared but the height is on its own.

So don't you you want the radius to be as large as possible?

ooh … got to go now … Doctor Who starting on telly!

 

[Amith2006]

Hi Amith2006!


Yes, the radius is squared but the height is on its own.

So don't you you want the radius to be as large as possible?

ooh  got to go now  Doctor Who starting on telly!

so doed it seem ok?

 

[tiny-tim]

so does it seem ok?

No!

You want the radius to be as large as possible,

but you've made it the smallest possible (5).

Try again, and see the difference!

 

[Amith2006]

You want the radius to be as large as possible,

but you've made it the smallest possible (5).

The problem that i face is that i can't cut out a circle of diameter 20 inches because the height is only 10 inches. i can only do so by making the Cross Section oval.

 

[tiny-tim]

The problem that i face is that i can't cut out a circle of diameter 20 inches because the height is only 10 inches. i can only do so by making the Cross Section oval.

No … draw a diagram … 6 bricks in two layers of 3.

One side is 2 bricks x 3 bricks.

Draw the circle on that side!

(btw, what happened to π in the formula?)

 

[Amith2006]

thanx.