Question

How many spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal 11dm × 1 m × 5 dm?

Answer 1

Answer:

The numbers of spherical bullets formed are 8400.

SOLUTION :

Given : Dimension of rectangular metallic block = 11dm × 1m × 5dm

and diameter of each  spherical  bullet = 5 cm

Dimension of rectangular metallic block = (11/10) m × 1m × (5/10)m = 1.1 m × 1 m × 0.5 m  

[1 dm = 1/10 m]

Radius of each  spherical  bullet =  5/2 cm = 2.5 cm = 2.5 /100 = 0.025 m = 25 × 10^-³ m

[1 cm = 1/100 m ]

Volume of rectangular metallic block = 1.1 m × 1 m × 0.5 m = 0.55 m³ = 55 × 10^-² m

Volume of rectangular metallic block = 55 × 10^-² m

Volume of the sphere =  4/3πr³

Volume of the sphere = 4/3 × 22/7 ×(25 × 10^-³ )³

Number of bullets  = Volume of the rectangular block / volume of the spherical bullets

= 55 × 10^-²  / 4/3 × 22/7 × (25 × 10^-³ )³

= 55 × 3 × 7 × 10^-²+^9 / 4 × 22×  25 × 25 × 25

= (3 × 7) × 10^7 / 8 × 5 × 625

= 21 × 10^7/ 40 × 625

= 21 × 10^7/ 25000

= 21 × 10^7/ 25 × 10³

= 21 × 10^7 × 10^-³ / 25

= 21 × 10⁴ / 25

= (21 × 10000)/25

= 21 ×  400

= 8400

Hence, the numbers of spherical bullets formed are 8400.

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Answer 2

Volume of block = 11 dm x 1 m x 5 dm = 110 cm x 100 cm x 50 cm = 550,000 cm3
Volume of bullet = 4/3*pi*r3 = 65.4 cm3 (approx).
Number of bullets = 550,000/65.4 = 8403.4 that is 8403


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