If 64 identical small spheres are made out of a big sphere of diameter 8 cm, what is surface area of each small sphere?

Let the diameter's of two sphere are d₁ and d₂, respectively.
? Ratio of their surface areas = 4?r₁²/4?r₂²
= (2r₁)²/(2r₂)² = d₁²/d₂²
= (d₁/d₂)² = (3/5)² = 9/25 = 9 : 25

Curved surface area of the sphere = 4?r²
or 616 = 4?r²
? ?r² = 616/4 = 154
? r² = (154 x 7) / 22 = 49
? r = ?49 = 7 cm
? Volume of the sphere = (4/3)?r³
= (4/3) x (22/7) x 7 x 7 x 7
= 4312 / 3 cm³

Curved surface area of the hemisphere = 2?r²
= 2 x (22/7) x (7/2) x (7/2) = 77 sq
As bowl is to painted inside and outside.
? Total surface to be painted = 77 x 2 = 154 sq cm
? Cost of painting 154 sq cm = (5/10) x 154 = 1/2 x 154 = ? 77

Radius of the sphere = 16/2 = 8 cm
Volume of the sphere = (4/3) x ? x 8 x 8 x 8 cm³
Radius of each lead ball = 2/2 = 1 cm
Volume of each lead ball = Volume of sphere / Volume of lead ball
= (4/3) ? x 1 x 1 x 1 = 4?/3 cm³
? Number of lead balls = [(4/3) x ? x 8 x 8 x 8 x 3] / [4 ?]
= 8 x 8 x 8 = 512

According to the question,
Surface area of sphere = Surface area of hemisphere
4?r₁² =3?r₂²
? r₁/r₂ = ?3/2
? Ratio in volume = [(4/3)?r₁³] / [(4/3)?r₂³]
= 3?3/8 : 1

Curved surface area = 2?r²
= 2? x 14 x 14 = 2 x (22/7) x 14 x 14
= 2 x 22 x 2 x 14
= 88 x 14
= 1232 sq cm

Given,
Diameter = 2 cm
? r = 1 cm
Now, Total surface area of hemisphere = 3?r²
and curved surface area = 2?r²
Required difference = 3?r² - 2?r² = ?r²
= ? x 1² = ? sq cm

Let radius of the third sphere be r.
Then, 4/3 ? x (12)³ = 4/3 ? x (6)³ + 4/3? x (8)³ + 4/3 ?r³
? (12)³ = (6)³ + (8)³ + r³
? r³ = 1728 - 216 - 512
? r³ = 1000
? r = 10 cm

According to the formula
Percentage increase in surface area = [ 2x + x²/100]%
= [2 x 3 + (3)²/100]%
= [6 + 0.09]%
= 6.09%

According to the formula,
Percentage decrease in surface area = [2 x (-24) + (-24) x (-24)/100]%
= [-48 + 5.76]% = - 42.24%