If a solid right circular cylinder made of iron is heated to increase

1.	If a solid right circular cylinder made of iron is heated to increase its radius and height by 1% each, then by how much per cent is the volume of the solid increased?
Answer» Let r and h be the radius and height of the cylinder respectively. Then, after 1% increase, New radius = 1.1 r and new height = 1.1 h Original volume = πr²h , New volume = π(1.01r)² (1.01h) =1.030301 πr²h ∴ % increase = \(\bigg(\frac{1.030301πr^2h-πr^2h}{πr^h}\times100\bigg)\)% = \(\bigg(\frac{0.030301πr^2h}{πr^h}\times100\bigg)\)% = (0.030301 × 100)% = 3.03% Volume of solid cylinder V= πr²h If initial radius and height are 100cm each then increased radius and height will be 101cm each. Initial volume V₁=π×100×100² ^{Increased volume V₂}= π×101×101² Percentage increase =[ (V2-V1)/V1]×100 =(101^3-100^3)/100^3×100 = 3.0301%

If a solid right circular cylinder made of iron is heated to increase its radius and height by 1% each, then by how much per cent is the volume of the solid increased?

Answer»

Let r and h be the radius and height of the cylinder respectively. Then, after 1% increase,

New radius = 1.1 r and new height = 1.1 h

Original volume = πr²h ,

New volume = π(1.01r)² (1.01h) =1.030301 πr²h

∴ % increase = \(\bigg(\frac{1.030301πr^2h-πr^2h}{πr^h}\times100\bigg)\)% = \(\bigg(\frac{0.030301πr^2h}{πr^h}\times100\bigg)\)%

= (0.030301 × 100)% = 3.03%

Volume of solid cylinder V= πr²h

If initial radius and height are 100cm each then increased radius and height will be 101cm each.

Initial volume V₁=π×100×100²

^{Increased volume V₂}= π×101×101²

Percentage increase

=[ (V2-V1)/V1]×100

=(101^3-100^3)/100^3×100

= 3.0301%