Question

What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?

Answer 1

Here, r = Internal radius
        R = External radius = 10 cm
        h = Length of the cylinder
        t = Thickness = 0.25 cm
Volume of the hollow cylinder = πh(R² - r²) = π (16) (10² - (10-0.25)²) = 79 π cm³
Volume of the solid cylinder = Volume of the hollow cylinder
We know that the radius of the solid cylinder is 1 cm.
∴ π(1²)h = 79 π​
h = 79 cm
Hence, length of the solid cylinder that gives the same volume as the hollow cylinder is 79 cm.