Indian Institute of Foreign Trade 2016 Solved Paper

Question : 12 of 123

Marks: +1, -0

A right circular cylinder has a height of 15 and a radius of 7. A rectangular solid with a height of 12 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. The volume of the liquid is

147(5π - 8)
180(π - 5)
49 (5π - 24)
49(15π - 8)

Validate

Solution:

(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)

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