The volume of a cube and a cuboid are 216 cubic cm and 480 cubic cm respectively. If the length and breadth of cuboid are in the ratio 5 : 4 and the height of cuboid is equal to the length of side of cube, then find the ratio of face diagonal of cube to the diagonal of cuboid.

Correct option is A

Given:

Volume of a cube and a cuboid are 216 cubic cm and 480 cubic cm respectively.

Ratio of  length and breadth of cuboid = 5 : 4

Height of cuboid = side of cube

Formula Used:

Volume of cuboid = length × width × height

Volume of Cube = $$Side^3$$​​

Explanation:

Height of the cuboid = side of the cube = ∛216 = 6 cm
Let the length & breadth of the cuboid be 5x & 4x respectively.
5x × 4x × 6 = 480
x = 2
5x = 10
4x = 8
Face diagonal of the cube = 6√2 cm
Diagonal of the cuboid = √(10)2 + 82 + 62 = 10√2 cm
Required ratio = 6√2 : 10√2 = 3:5