Question 1110548
SOLUTION:{{{highlight(7cm)}}}
 
STEPS:
A cross section of box or diameter {{{d}}} and the pencil, with lengths in cm,would look like this
{{{drawing(100,280,-1.5,8.5,-2,26,
rectangle(0,0,7,24),locate(7.2,13,24),
rectangle(7,0,6.5,0.5),locate(3.5,12,red(25)),
locate(3,0,d),red(line(0,0,7,24))
)}}} Applying the Pythagorean theorem to the right triangle,
{{{d^2+24^2=25^2}}}
{{{d^2=25^2-24^2}}}
 
If you have studied polynomials,
you know that {{{25^2-24^2=(25-24)(25+24)=1*49=49=7^2}}} .
 
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^2=625-576}}}
{{{d^2=49}}}
{{{d=sqrt(49)}}}
{{{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.