SOLUTION: what is the length of the longest pole that can be put into a room of dimensions 10m�10m�5m. also find the volume of the pole if its radius is 70cm

Question 1011125: what is the length of the longest pole that can be put into a room of dimensions 10m�10m�5m. also find the volume of the pole if its radius is 70cm
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The room, with the pole, ,
and the pole's shadow, , would look like this:

=length of AB, and =length of AB, both in meters.
On the floor of the room, is the diagonal of a 10m�10m square
(or the hypotenuse of a right triangle with legs measuring ,
so the Pythagorean theorem tells us that
.
On an imaginary vertical plane, triangle is a right triangle,
and its legs' length, in meters, are
and .
So the length, in meters, of hypotenuse is
.
That is the length of the longest pole that can be put into a room of dimensions 10m�10m�5m,
provided that the pole is pencil-thin or thinner.

If the pole is wider than pencil-thin its ends will not go all the way into corners and , =
so it would need to be a bit shorter,
but I do not think that you are expected to do real world calculations,
as an engineer would do,
so the expected answer to the second question is the volume of a pole/cylinder
that is long and in radius.
For a cylinder of radius and height , the volume is
,
so for your problem, the volume of the pole in cubic meters is
.
That is about .
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