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...
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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.
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.
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