A drainage tile is a cylindrical shell 21 cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively. What is the volume of clay required for making a tile?

$30.24\, π\, cm^3$

The correct answer is Option (1) → $30.24\, π\, cm^3$

A drainage tile is a cylindrical shell, so the volume of clay required is the difference of volumes of two cylinders.

Given:

• Length (height), h = 21 cm
• Outside diameter = 5.1 cm ⇒ Outer radius, R = 2.55 cm
• Inside diameter = 4.5 cm ⇒ Inner radius, r = 2.25 cm

Formula:

$\text{Volume} = \pi h (R^2 - r^2)$

Calculation:

$R^2 = (2.55)^2 = 6.5025$

$r^2 = (2.25)^2 = 5.0625$

$R^2 - r^2 = 1.44$

$\text{Volume} = \pi \times 21 \times 1.44 = 30.24\pi \text{ cm}^3$