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The radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained?

The radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained? Correct Answer 83

Volume of the solid cylinder = πr2h = 22/7 × 7 × 7 × 21 = 3234

When bullets are formed;

Radius of base of cylindrical part of bullet = r1 = 2.1 cm

Radius or height of hemispherical part of the bullet = r2 = 2.1 cm

∴ Height of the cylindrical part of bullet = 3.5 – 2.1 = 1.4 cm

Volume of one bullet = πr12h + 2/3 × πr23

⇒ 22/7 × (2.1 × 2.1 × 1.4 + 2/3 × 2.1 × 2.1 × 2.1)

⇒ 22/7 × (6.174 + 6.174)

⇒ 38.808

∴ Approximate number of bullets = 3234/38.808 = 83.33 ≅ 83

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