Final answer:
To find the volume of the rectangular solid, we first calculate the values of the width and height using the given relationship. Then, we use the formula for volume (V = length x width x height) to find the volume of the rectangular solid. The correct answer is 90 (option C).
Step-by-step explanation:
To find the volume of the rectangular solid, we need to first find the values of the width (w) and the height (h). We can do this by using the given relationship w³h³ = 27. By taking the cube root of both sides of the equation, we get w³ = h³ = 3. Therefore, w = h = 3.
The volume of a rectangular solid is given by V = length x width x height. Substituting the given length of 10 and the values of w and h, we have V = 10 x 3 x 3 = 90.
Therefore, the volume of the rectangular solid is 90, so the correct answer is C. 90.