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?
Answer & explanation
Correct answer: option 1
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:
$R^2 = (2.55)^2 = 6.5025$
$r^2 = (2.25)^2 = 5.0625$
$R^2 - r^2 = 1.44$
$\text{Volume} = \pi \times 21 \times 1.44 = 30.24\pi \text{ cm}^3$