Cubes Math
math challegnq uesiton cubes and rectuanglar solids?
a rectnagular solid has dimensions 7 in, 5 in, 1 in. if the main diagonal of this solid has the sme length as the main diagonal of a cube, fin dth voluem fo the cube in cubic inches
why is it 125 expalinand shwot steps
The diagonal of the box is the hypotenuse of a triangle that has one side as the height of the box, and the other side is the diagonal of the base. So, the diagonal of the base by using the Pythagorean Theorem is sqrt(l^2+w^2). So, the diagonal of the box is sqrt(l^2+w^2+h^2)
In this case, this means that the diagonal of the box is sqrt(49+25+1)=sqrt(75)=5sqrt(3)
Now, a cube has the same length all around, so by using the above formula, a cube's diagonal should be sqrt(s^2+s^2+s^2)=sqrt(3s^2)=s*sqrt(3)
So, since the diagonal of the first box is 5sqrt(3), the cube with the same sized diagonal would have a side length of 5, and the volume would be 5^3 or 125
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(653 words , Copyright May 2006 Ugur Akinci)
by Ugur Akinci, Ph.D.
Creative Copywriter and Technical Communicator
Ugur Akinci, Ph.D. is a Creative Copywriter, Editor, an experienced and award-winning Technical Communicator specializing in fundraising packages, direct sales copy, web content, press releases and hi-tech documentation.
He has worked as a Technical Writer for Fortune 100 companies for the last 7 years.
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