What is the volume of a cube whose body diagonal measures 33 cm?  Ops:   A. 18 cm3    B. 243 cm3    C. 27 cm3    D. 81 cm3

The volume of a cube can be found using the formula V = s^3, where s is the length of a side of the cube.

However, we are given the length of the body diagonal, not the side. The relationship between the body diagonal (d) and the side length (s) of a cube is given by the formula d = s*sqrt(3).

So, we can find the side length by rearranging this formula to s = d/sqrt(3).

Substituting the given body diagonal length of 33 cm, we get s = 33/sqrt(3) = 19.05255888325765 cm.

Now, we can find the volume by substituting s into the volume formula:

V = (19.05255888325765 cm)^3 = 6892.177448948 cm^3.

So, the volume of the cube is approximately 6892 cm^3. This option is not listed in the given choices.