The perimeter of the triangular base of a right prism is 60 cm and the sides of the base are in the ratio 5 : 12 : 13. Then, its volume will be (height of the prism being 60 cm).?

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

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

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%

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

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

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.

Ratio of curved surface area of cylinder and cone = [2?rh] / [?r?h² + r²]
= [2 x 6 x 8] / [6 x ?6² + 8²]
= 96/(6 x 10) = 96/60 = 8/5 = 8 : 5

Let required number of coins be n, Then,
n x 1/3 x ? (1/10)² x 1 = ? x (3)² x 5
? n = 9 x 5 x 3 x 100 = 13500

Volume of 1 bullet = 4/3?(2)³ = (32/3 x 22/7) cm³
Volume of the cube = (44)³
? Number of bullets = Volume of solid/Volume of 1 bullet
= (44)³ x 3 x 7 / 32 x 22 = 2541

Let r = Radius of cylinder = Radius of sphere, h = Height of the cylinder.
According to the question.
4/3?r³ = ?r²h
? h = 4r/3
? 4r = 3h
? 2r = 3/2h
? 2r/h = 3/2
? Required ration = 3 : 2