Question

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​

Answer 1

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 2

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.