my math teacher said that the diagonal of the face of a given cube can be solved by the formula d=s√2 then she said that the diagonal of the cube is equal to a diagonal of a face. How can i prove that she is wrong?
2007-08-04 21:30:30 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Hi,
Yes, you can prove she is wrong.
The diagonal of a cube is found by
.........________
d = √s² + s² + s² or
.........___
d = √3s² =
..........._
d = s√3
This is the formula for the diagonal of the cube.
I hope this helps!! :-)
2007-08-04 21:38:26 · answer #1 · answered by Pi R Squared 7 · 0⤊ 1⤋
I think this is an example of failure to define terms. If you have a cube with edges of length s:
Face diagonal is of length sâ2.
Body diagonal is of length sâ3.
I suspect your teacher would readily agree with the above.
The question is, what is meant when someone just says diagonal? I would tend to think "body diagonal." Are you sure you heard what she said correctly? Could she have said that you can calculate the diagonal of a cube with the diagonal of a face and an edge? That's not the same thing as saying the diagonal of a cube is equal to the diagonal of a face.
2007-08-05 04:54:14 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
The diagonal of the face of a cube is sâ2
The diagonal of the cube is sâ3
The diagonal of the face of a cube, an edge of the cube and the diagonal of the cube form a right-angled triangle. Use Pythagoras' Theorem to get the diagonal of the cube
= sqrt((sâ2)^2 + (s)^2) = sâ3
2007-08-05 04:36:22 · answer #3 · answered by gudspeling 7 · 1⤊ 0⤋
your math teacher said that the diagonal of the face of a given cube can be solved by the formula d=sâ2 then she said that the diagonal of second cube is equal to a diagonal of the face of the first cube. find the edge of the second cube!
are you gaping in the class?
2007-08-05 05:14:20 · answer #4 · answered by Anonymous · 1⤊ 0⤋
diagonal of a cube is always greaer than the diagonal of the face.becoz. diagonal of cube is aâ3 where as diagonal of face of a cube is aâ2
2007-08-05 05:07:01 · answer #5 · answered by rajesh m 1 · 0⤊ 0⤋
no they are different. the diagonal of the face is shorter than the diagonal of the cube.
eg if you have a 5cm cube the diagonal of the face will be 7.07cm.
the diagonal of the cude will on the other hand be 8.66 cm.
2007-08-05 04:46:51 · answer #6 · answered by kwaku b 1 · 0⤊ 0⤋
I don't think it's possible. Seeing how a cube is built out of 6 regular quadrilaterals. the space from one vertex in a face to the other. Would be the same as one vertex of a face. To the opposite vertex of the opposite face. Of course I could be wrong
2007-08-05 04:35:14 · answer #7 · answered by Richard S 2 · 0⤊ 1⤋
Check out this solution...
http://mathcentral.uregina.ca/QQ/database/QQ.09.04/brett1.html
2007-08-05 04:35:46 · answer #8 · answered by Anonymous · 0⤊ 0⤋