8. Determine the diagonal distance across a side of a cube with volume 100 cm3.

A. 6.56 cm

B. 7.07 cm

C. 14.14 cm

D. 16.67 cm

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The volume of the cube (v)= (side)^3= s^3

100 = S^3

==> s= (100)^1/3 = 4.643

Now to calculate the diagonal (d):

We know that:

d^2= s^2 + s^2

= 2s^2= 2(4.643)^2= 43.1148

==> d = sqrt(43.1148)

= 6.566

Then the answer is A.

The volume of a cube is given by the formula:

Volume of a cube= L^3

Where: L = Length of a side of the cube:

Substituting the given value of volume of cube in the above formula:

100 = L^3

Therefore:

L = 100^(1/3)

Diagonal distance along the side of a cube with length of side equal to L is given by:

Length of diagonal of a side of diagonal = (2*L^2)^1/2

Substituting the value of L calculated in formula for length of diagonal:

Length of diagonal of a side of diagonal = {2*[100^(1/3)]^2}^1/2

= [2*100^(2/3)]^1/2

= 6.5642 cm

Thus from the given options the correct answer is Option A.

The cube of 100 cm^3 has a side (100cm^3)^(1/3) = 100^(1/3) cm = k

So the diagonal accross a side = sqrt(k^2+k^2) = sqrt(2k^2) = (sqrt2)k

= 2^(1/2)(100^(1/3) = 6.56cm. So a is the choice.

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