A room is in the shape of cube and the length of the longest rod placed in it is $21\sqrt{3}$cm. The area of the floor is:
Answer & explanation
Correct answer: option 1
We know that,
Diagonal of cube = Side\(\sqrt {3}\)
Area of floor = Side2
We have,
Length of the longest rod = 21\(\sqrt {3}\) m.
Length of the longest rod of cube = Diagonal of cube = \(\sqrt {3}\) × Side of cube
21\(\sqrt {3}\) = Side\(\sqrt {3}\)
Side = 21 m
Area of floor = = 212 = 441 m2.