Indian Institute of Foreign Trade 2016 Solved Paper

(a) The Volume of Cylinder = 15 × 49π
The rectangle solid is placed in cylinder such that each of the corners of solid is tangent to walls of cylinder.
Hence the diameter of cylinder is equal to diagonal of the square base.
∴As the diameter of cylinder is 14, so diagonal of square is 14 and hence side of square is 7√2.

Volume of rectangular solid = 7√2×7√2×12=98×12
∴Volume of liquid = 15 × 49π – 98 × 12
= 147 (5π – 8)