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