Discussion
The diagonal of a cubic room is \(11\sqrt{3}\) feet. Find the volume of it.
Answer: D
The diagonal of a cube of side a is \(a\sqrt{3}\), so \(a\sqrt{3}=11\sqrt{3}\) gives a = 11 feet.
The volume is 11 cubed = 1331 cubic feet, option D. The options with the root of 3 come from multiplying the diagonal rather than the side.
The space diagonal d of a cube of side a is \(a\sqrt{3}\), which follows from Pythagoras applied twice. With d = \(11\sqrt{3}\) the side is 11 feet, and the volume is 11 x 11 x 11 = 1331 cubic feet. The options with a root of 3 would apply if the diagonal was used as a side.
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