If radius of a sphere is decreased by 24%, by what per cent does its surface area decrease?

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

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

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

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

Volume of small spheres
= Volume of bigger sphere / Number of small spheres = [(4/3)?(4)³] / 64
= [(4/3) x ? x 4 x 4 x 4] / 64
= 4/3 ? cm³

Let radius of small sphere be r
? 4/3?r³ = 4?/3
? r² = 1 cm
Now, surface area of small sphere = 4?r² = 4? cm²

Here, n = 100%
According to the formula
Percentage increase in volume = [(1 + n/100)³ - 1] x 100%
= [(1 + 100/100)³ - 1] x 100%
= [8 - 1] x 100% = 700%

Volume of solid sphere of radius 4 cm = (4/3)?(4)³ cm³
Volume of hollow sphere = 4/3?[(8)³ - (6)³] cm³
? Weight of 4/3?(4)³ cm³ = 4 kg
= 4(512 - 216)/4³ = 18.5 kg

Volume of prism = Area of base x Height
= (1/2) x 10 x 12 x 20
= 1200 cm²

? Weight of prism = 1200 x 6
= 7200 g
= 7.2 kg

Let the sides of the base are 5k, 12k and 13k, respectively.
Given, perimeter of base = 60 cm
? 5k + 12k + 13k = 60
? k = 60/30 = 2
The sides of base are 10 cm, 24 cm 26 cm.
? Volume of prism = (1/2) x 10 x 24 x 50 = 6000 cm³

Volume of the prism = (Area of the base ) x (Height)
Volume of the pyramid = 1/3 (Area of the base ) x (Height)
Required ratio = [A x H] / [(1/3) x A x H]
Therefore, Ratio of the volumes of the prism and the pyramid = 3 : 1.