Question

Find the length of a solid cylinder of diameter 4 cm when recast into a hollow cylinder of outer diameter 10 cm, thickness 0.25 cm and length 21 cm? Give your answer correct to two decimal places.

Answer 1

For the solid cylinder:
diameter = 4cm
radius = 2cm
Let its length be l.
Volume of solid cylinder
= πr²l
= π2²l
= 4πl cm³
For the hollow cylinder:
Outer diameter = 10cm
Outer radius(R) = 5cm
Inner radius(r) = R - thickness
r = 5 - 0.25
r = 4.75cm
Volume of the hollow cylinder
= πR²h - πr²h
= πh (5² - 4.75²)
= π x 21(25 - 22.5625)
= 51.1875π cm³
Since the solid cylinder is recast into a hollow cylinder,
Volume of solid cylinder
= Volume of material in the hollow cylinder
4πl = 51.1875π

l = `(51.1875π)/(4π)`
l = 12.80cm
∴ The length of the solid cylinder is 12.80cm.