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Some number of hexagonal pens shaped as prism are put in a cylindrical box of radius 9 cm and height 7 cm. If the remaining volume is 328.8 cm3 then how many pens were put in the box if side of hexagonal base of the pen is 1 cm and height of a pen is 7 cm. (Take √3 = 1.73)

Some number of hexagonal pens shaped as prism are put in a cylindrical box of radius 9 cm and height 7 cm. If the remaining volume is 328.8 cm3 then how many pens were put in the box if side of hexagonal base of the pen is 1 cm and height of a pen is 7 cm. (Take √3 = 1.73) Correct Answer 80

Volume of the cylindrical box = 22/7 × 9 × 9 × 7 = 1782 cm3

Volume of a pen = 6 × √3/4 × 1 × 1 × 7 = 18.165 cm3

Since the remaining volume = 328.8 cm3

⇒ Volume of all the pens = 1782 - 328.8 = 1453.2 cm3

∴ Number of pens = 1453.2/18.165 = 80

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