SOLUTION: A thin pencil will only fit into a cylinder of height 24cm. If a pencil is 25cm long, what is the diameter of the cylinder?

Question 1110548: A thin pencil will only fit into a cylinder of height 24cm. If a pencil is 25cm long, what is the diameter of the cylinder?

Found 2 solutions by stanbon, KMST:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A thin pencil will only fit into a cylinder of height 24cm. If a pencil is 25cm long, what is the diameter of the cylinder?
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Sketch the picture::
You have a right triangle with height = 24, hypotenuse = 25, and base = b
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b = sqrt[25^2-24^2] = 7
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Cheers,
Stan H.
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Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
SOLUTION:

STEPS:
A cross section of box or diameter and the pencil, with lengths in cm,would look like this
Applying the Pythagorean theorem to the right triangle,

If you have studied polynomials,
you know that .

If you had a list of Pythagorean triples handy
you would know see in that list that in a right triangle with
hypotenuse length and a leg/side of length
the other leg/side length id .
(You can do an internet search for Pythagorean triples
and will have the sets of 3 integers that can be side length of a right triangle).

If using one of the options above would tell your teacher
that you asked for help with this problem,
the next steps to the solution would be

WARNING: Relying too much on outside help to solve problems will make you dependent on help from others. One of my children found that to be a problem when he got to college.
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