Question

a hollow cylinder of height 3 cm is recast into a solid cylinder of height 9cm. if the external and internal radii of hollow cylinder are 4.3 cm and 1.1 cm then find the radius of the solid cylinderResults in English

Answer 1

volume of hollow cylinder = volume of solid cylinder
Let external radius of hollow cylinder = R = 4.3 cm
internal radius of hollow cylinder = r = 1.1 cm
Length of hollow cylinder = L = 3 cm

Let radius of solid cylinder = R₁
Length of solid cylinder = L₁ = 9 cm

π (R² - r²) × L = π R₁²L₁
(4.3 - 1.1)(4.3 + 1.1) × 3 = R₁² × 9
3.2 × 5.4 × 3 = R₁² × 9
3.2 × 1.8 = R₁²
taking square root both sides,
R₁ = 8 × 0.3 = 2.4 cm

Hence, radius of solid cylinder is 2.4 cm