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?

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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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
SOLUTION:highlight%287cm%29

STEPS:
A cross section of box or diameter d and the pencil, with lengths in cm,would look like this
Applying the Pythagorean theorem to the right triangle,
d%5E2%2B24%5E2=25%5E2
d%5E2=25%5E2-24%5E2

If you have studied polynomials,
you know that 25%5E2-24%5E2=%2825-24%29%2825%2B24%29=1%2A49=49=7%5E2 .

If you had a list of Pythagorean triples handy
you would know see in that list that in a right triangle with
hypotenuse length 25 and a leg/side of length 24
the other leg/side length id 7 .
(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
d%5E2=625-576
d%5E2=49
d=sqrt%2849%29
d=7

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.