Discussion

Explanation:

Volume of liquid = volume of cylinder – volume of rectangular solid

Volume of cylinder = ๐œ‹r2h = (72)(15)= 735๐œ‹

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œ‹ – 1176

= 147(5๐œ‹ – 8)

Hence, option (a).

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