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
Explanation:
Volume of liquid = volume of cylinder – volume of rectangular solid
Volume of cylinder = ๐r2h = (72)(15)= 735๐
Since each corner of the solid with a square base is tangential to the cylinder wall, the diagonal of the square base is equal to the diameter of the base of the cylinder.
∴ Diagonal of square base = 2(7) = 14
∴ Side of square = 14/√2 = 7√2
Volume of rectangular solid = (7√2) × (7√2) × 12 = 1176
∴ Volume of liquid = 735๐ – 1176
= 147(5๐ – 8)
Hence, option (a).
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