2007-03-08 10:32:23 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A pencil that fits along the box's diagonal, from a lower corner to the opposite upper corner. Put the lower corner at the origin, then the opposite corner has coordinates (4, 6, 3). The distance from the origin to (4, 6, 3) is
Squareroot(4^2 + 6^2 + 3^2) = Squareroot(61) = 7.81 or so,
so a pencil 7.81" long.
2007-03-08 10:39:08 · answer #1 · answered by brashion 5 · 0⤊ 0⤋
Volume of the box is 72 inches cube. But, you need the longest pencil. For the longest pencil to be able to fit into the box, you need the longest diagonal line that can fit into the box. The box had a length of 6" and Height of 4", you can put the longest pencil possible which is 7.21"...
2007-03-08 18:39:23 · answer #2 · answered by Plasma 2 · 0⤊ 1⤋
The Pythagorean Theorum works in 3 dimentions:
sqrt(4^2 + 6^2 + 3^2) = sqrt (61) = 7.8"
2007-03-08 18:36:55 · answer #3 · answered by John S 6 · 0⤊ 0⤋
sqrt 54 = 7.35 inches
(Diagonal across the box starting from the corner of where 4" meets 6".)
2007-03-08 18:37:58 · answer #4 · answered by Mathematica 7 · 0⤊ 1⤋