The radius and the height of a cylinder are increased by 50% and 75% respectively. Express the original volume as a percentage of the volume obtained.

Given:The radius and the height of a cylinder are increased by 50% and 75% respectivelyFormula used:Volume of a cylinder, V = π × r2 × hCalculation:Let r1 and h1 be the increased radius and height respectively⇒ r1 = R + (r × (50/100)) = 1.5r⇒ h1 = H + (h × (75/100)) = 1.75hVolume obtained, V1 = π × r1 × r1 × h1 = π × (1.5r)2 × (1.75h)⇒ V1 = 3.9375 × π × r2 × hNow,(V/V1) × 100 = [(π × r2 × h)/(3.9375 × π × r2 × h)] × 100⇒ (1/3.9375) × 100 = 25.39%Radius is increased by 50%Height is increased by 75%Calculation:Let the initial radius be 2 units⇒ New radius = 150/100 × 2 = 3 unitsLet the initial height be 4 units⇒ New height = 175/100 × 4 = 7 units Initial volume = π × (2)2 × 4⇒ Initial volume = 16π New volume = π × (3)2 × 7⇒ New volume = 63π REQUIRED PERCENTAGE is,⇒ (16π/63π) × 100 ⇒ 25.39 ∴ The percentage is 25.39%