Question

Volume of material used in constructing a hollow cylinder of height 24 cm and thickness 1 cm is 96π. What isthe sum of the internal and external radii?​

Answer 1

Answer:

The volume of the hollow cylinder, V = 96π cubic cm

Height, h = 24 cm

Thickness, t = 1 cm  

Let the outer radius be “R” and inner radius be “r”.

Inner radius, r = (R – 1) cm ….. [∵ thickness = 1 cm ∴Inner radius = outer radius - thickness]

The Volume of a hollow cylinder is given as,

V = (Volume of the external cylinder) – (Volume of the Internal cylinder)  

⇒ V = π * h * (R² – r²) ….. (i)

Substituting the given values in eq. (i), we get

96π = π * 24 * [R² – (R-1)²]

Or, 4 = R² – R² + 2R - 1

Or, 2R – 1 = 4  

Or, 2R = 5

Or, R = 5/2 = 2.5 cm

∴ Inner radius, r = R – 1 = 2.5 – 1 = 1.5 cm

Thus,  

The sum of the internal and external radii = R + r = 2.5 + 1.5 = 4 cm .