Find the volume of a cube on which the diagonal of a face measures 2.?

Question

Please explain how to do it

Answer 1

The faces are squares. In a square, the diagonal is
d = sqrt2 * s, where s is the side. We have d=2, so
2 = sqrt2 * s
→ s = 2/sqrt2 = sqrt2.

The volume of the cube is s³ = 2^(3/2).

Answer 2

Edit: I DO apologise - I have made a grave error!

This is a correction

The volume is 2.8284 units cubed

By pythagoras' theorem A^2 + B^2 = C^2

since the diagonal is 2 therefore :
A^2 + B^2 = 2^2
or
A^2 + B^2 = 4
since it is a cube, the sides are all equal
which means A and B are equal. thus... B=A

So the equation is A^2 +A^2 =4
therefore A^2 MUST be 2
That is......................................(2+ 2 = 4)


Therefore A = square root of 2


volume of a cube is length * height * depth
and since the side are all equal sqrt 2* sqrt 2* sqrt 2= 2.8284 units cubed


Hope this makes sense

Answer 3

If the diagonal is 2, then the sides are all "sqrt(2) / 2". Now, cube this value, and you have your answer: sqrt(8) / 8 = sqrt(2) / 4

Answer 4

treat the diagonal face as a seperate triangle find the length of the two remaining sides of the triangle using a2+b2=c2. Use the length of the sides to find the volume of the cube.

Answer 5

The formula to find the diagonal is:

d = s * sqrt(2)
where d = the diagonal and s is the length of one side.
In this case, we know that d= 2, so we must solve for s.

2= s * sqrt(2)
divide both sides by sqrt(2).
s= 2/(sqrt(2))
s = sqrt(2)
The length of one side = sqrt(2)
The volume of a cube is L*W*H.
sqrt(2)^(3) = sqrt(2) *sqrt(2)*sqrt(2) = ~2.8284

Answer 6

Since the diagonal measures 2, the side must measure √2 (Pythagorean Theorem) so the volume is (√2)^3 = 2.828 units.

HTH

Doug

Answer 7

well the diagnal would be the hypotnuse of a traiangle and the other 2 sides are equal since it is a cube. therefor Xsq + X sq = 2sq
Xsq + Xsq = 4
2xsq = 4
xsq = 2
x=1.4142136

now you know the dimensions of the cube all sides are 1.4142136. to find the volume you take wxhxd all being 1.4142136

so the answer when multiplied out is 2.828 cubic units.

Answer 8

2*side^2=2^2
2*side^2=4
side^2=2
side=sqrt(2)

volume=side^3=
sqrt(2)^3=
2sqrt(2)=
2.8284271247461900976033774484194