Question

can you guys help me out of this?
An object in which the ends are regular hexagons was cut from a cylindrical wooden solid of length 24 inches and 1.3 inches in diameter. Find the volume of the said object with the least waste material that can be taken from the wood.

Answer 1

Hi! So, how well do you understand the situation, for starter?

Answer 2

for starting*

Answer 3

You start wit this:
Your end shape is this:
The face of it will look like this:
The least wasteful you can be is to have the shape take up as much room as it can. Then the rest (the waste) is less.The side length is the radius, which is \(\frac{1}{2}\) the diameter.
The formula for the hexagon area is \(\dfrac{3\sqrt 3}{2}s\) where \(s\) is the length of a side.
The volume of this would be the area multiplied with the length.
The waste volume is the difference between the volume of the whole cylinder and the volume of this new shape.