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A 20 cm high gift piece made up of glass is formed by mounting a pyramid with square base of side 8 cm above a cubical shaped figure. How many such complete pieces can be formed by melting a cylindrical shaped glass piece with base radius 12 cm and height 14 cm?

A 20 cm high gift piece made up of glass is formed by mounting a pyramid with square base of side 8 cm above a cubical shaped figure. How many such complete pieces can be formed by melting a cylindrical shaped glass piece with base radius 12 cm and height 14 cm? Correct Answer 8

The cylindrical shaped glass piece has radius 12 cm and height 14 cm

⇒ Volume of the cylindrical shaped piece which is melted = πr2h

⇒ 22/7 × 122 × 14 = 6336 cm3

The small piece is consisting of cube of side 8 cm and a pyramid mounted on it

Side of cube = 8 cm, side of square base of pyramid = 8 cm and height of the pyramid = 20 – 8 = 12 cm

⇒ Volume of a small piece = Volume of cube + Volume of pyramid

⇒ Volume of a small piece = (Side)3 + 1/3 × (Area of base) × Height

⇒ 83 + 1/3 × 82 × 12

⇒ 512 + 256 = 768 cm3

⇒ Number of such pieces = 6336/768 = 8.25

∴ Total 8 complete pieces can be formed.

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