Question

A spherical solid ball of radius 8 mm is to be divided into eight equal parts by cutting it four times
longitudinally
along the same axis. Find the surface area of each
of the final pieces thus obtained (in mm^2) ?
(where pi= 22/7)​

Answer 1

Question :- A spherical solid ball of radius 8 mm is to be divided into eight equal parts by cutting it four times longitudinally along the same axis. Find the surface area of each of the final pieces thus obtained (in mm^2) ?

(where pi = 22/7)

Solution :-

we know that,

• when we cut the sphere solid ball into 8 pieces by cutting it four times longitudinally along the same axis , each piece will look like a slice of a orange.

so,

• Surface Area of each piece = (TSA of sphere/8) + πr² = (4πr²/8) + πr² = (1/2)πr² + πr² = (3/2)πr² .

then,

→ Surface area of each final pieces = (3/2) * (22/7) * 8 * 8 = (3 * 11 * 64) / 7 ≈ 301.7 mm². (Ans.)

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Answer 2

✩ Correct Question :

• A spherical solid ball of radius 8 mm is to be divided into eight equal parts by cutting it four times longitudinally along the same axis. Find the surface area of each of the final pieces thus obtained (in mm^2) ?(where pi= 22/7)

✩ Required Solution:

• Having one curved surface and two plane surfaces in each identical part ,

• Angle between the plane surfaces is 45°

⛤ Value given to us :

• Radio of ball (r) = 8mm

✩ According to question :

• Total surface area of one part = (1/8) of curved surface area of sphere + 2×Area of semi-circle.

• => (1/8) × 4πr² + 2×(1/2 × πr²)mm²

• => (1/2) × πr²+ πr²mm²

• => (3/2) × πr² mm²

✩ Putting. r = 8

• => (3/2)×π×(8)². mm²

• => 96 × 22/7 mm²

• => ⛤ 301.7 mm² (Answer )⛤ ✔

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