how many spherical balls of 2.5 mm diameter is can be obtained by melting a semiconductor disc of diameter 7 cm thickness 8 mm
Answers
Answer:
1881 Balls can be obtained
Step-by-step explanation:
Lets find volume of Semicircular Disc first
= Area of Semicircular disc* Thickness
Area of Semicircular disc = (1/2) π r²
π = 22/7 r = 7/2
Area of Semicircular disc = (1/2)(22/7) (7/2)² = 11 * 7 / 4 cm²
Thickness = 8mm = 8/10 cm = 4/5 cm
volume of Semicircular Disc = (4/5) * 11 * 7 / 4 = 77/5 cm³
Volume of one Spherical Ball = (4/3) π r³
r = 2.5/2 = 5/4 mm = 5/40 cm = 1/8 cm
= (4/3) (22/7) (1/8)³
= 11 / ( 21 * 64) cm³
Number of Spherical balls = (77/5) / (11 / (21 * 64)
= 77 * 21 * 64 / ( 5 * 11)
= 7 * 21 * 64 / 5
= 1881.6
1881 Balls can be obtained
answer : 1882
explanation : diameter of small ball = 2.5 mm
radius of small ball, r = 1.25 × 10^-3 m
diameter of disc = 7cm
radius of disc , R = 3.5 × 10^-2 m
thickness of disc , l = 8mm = 8 × 10^-3 m
let n spherical balls can be obtained by melting the semicircular disc.
so, n × volume of a spherical ball = volume of semicircular disc
⇒n × 4/3 πr³ = (1/2πR²)l
⇒n × 4/3 r³ = 1/2R²l
⇒n = 3R²l/8r³
= {3 × (3.5 × 10^-2)² × (8 × 10^-3)}/{8 × (1.25 × 10^-3)³
= {3 × 3.5 × 3.5 × 8 × 10^-7}/{8 × 1.25 × 1.25 × 1.25 × 10^-9}
= {3 × 3.5 × 3.5 × 10²}/{ 1.25 × 1.25 × 1.25}
= {3 × 35 × 35 }/{ 1.25 × 1.25 × 1.25}
= 1881.6 ≈ 1882
hence, 1882 balls can be obtained by melting the spherical balls.