The length of the largest possible rod that can be placed in a cubical room is 42√3m. The surface area (in m²) of the largest possible sphere that fit within the cubical room is: [Use π =22/7]
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 5544.
The length of the largest possible rod that can be placed in a cubical room is the diagonal of the cube.
Diagonal of the cube = 42√3 m
⇒ √3 × Length of the cube = Diagonal of the cube
⇒ √3 × Length of the cube = 42√3
Length of the cube = 42 m
The diameter of the sphere = Length of the cube = 42 m
⇒ Radius of the sphere = 42/2 = 21 m
The surface area of the largest possible sphere that fits within the cubical room = 4πr2 = 4 × (22/7) × 21 × 21 = 5544 m2