A solid metallic cube of side is $6 \sqrt[2]{4}$ cm, is melted and recast into a cuboid of length 12 cm and breadth 9 cm. What is the length (in cm) of the longest diagonal of the cuboid?
Answer & explanation
Correct answer: option 4
We know that,
Volume of cube = (side)3
Volume of cuboid = length × breadth × height
Length of diagonal of cuboid = \(\sqrt { l^2 + b^2 + h^2}\)
We have,
Side of cube = $6 \sqrt[2]{4}$ cm
Length of cuboid = 12 cm
Breadth of cuboid = 9 cm
Let diagonal = d
= Therefore, Volume of cube = Volume of cuboid
= ($6 \sqrt[2]{4}$ )3 = 12 × 9 × Height
= Height = \(\frac{6×6×6×4}{12×9}\) = 8 cm
= d = \(\sqrt { 12^2 + 9^2 + 8^2}\) = \(\sqrt { 144+81+64 }\) = 17 cm