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How can I figure the dimensions of a perfect cube if the hypotenuse through the center of the cube is 35cm?
Wiki User
∙ 12y ago
Somehow I messed up andused 31 instead of 35
That is why you are receiving an improvement
Do a Google search for Diagonal of a cube
Find this website.
mathcentral.uregina.ca/QQ/database/QQ.09.04/brett1.HTML - Draw a cube
You will see how to find the diagonal of a cube.
You use Pythagorean Theorem
Draw a cube
Label each side as s
Draw the diagonal of the base of the cube
Diagonal of base = (s^2 + s^2 )^0.5
Let the diagonal of the base be the horizontal side of the right triangle whose hypotenuse is the diagonal of the cube.
The height of the cube is the vertical side of the right triangle whose hypotenuse is the diagonal of the cube.
Now determine the length of the diagonal of the cube.
(diagonal of base)^2 + (height of cube)^2 = (diagonal of cube )^2
Diagonal of base = (s^2 + s^2 )^0.5….Height of cube = s
Use Pythagorean Theorem
(diagonal of cube )^2 = (diagonal of base)^2 + (height of cube)^2
(diagonal of base)^2 = [(s^2 + s^2 )^0.5]^2 = s^2 + s^2
height of cube)^2 = s^2
(diagonal of cube)^2 = (s^2 + s^2 + s^2)
(diagonal of cube )^2 = (3 * s^2)
diagonal of cube = (3 * s^2)^0.5 = 35
(3 * s^2)^0.5 = 35
Square both sides
3s^2 = 31^2 = 1225
s^2 = 408.33
s = 40833^0.5
s = 20.2 cm
Wiki User
∙ 12y ago
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