Question

The external radius of a metallic pipe is \(4\) cm and its internal radius is \(3\) cm. If its length is \(10\) cm, then the volume of metal is:

• A. \(120\ \text{cm}^3\)
• B. \(220\ \text{cm}^3\)
• C. \(440\ \text{cm}^3\)
• D. \(1540\ \text{cm}^3\)

Hint:

For a pipe (hollow cylinder), subtract areas first: \( \pi(R^2-r^2) \), then multiply by length \(h\).

Answer 1

The Correct Option is B

Step 1: Use the formula for volume of a hollow cylinder.
Volume \(V = \pi h (R^2 - r^2)\), where \(R\) is external radius, \(r\) is internal radius, and \(h\) is length.
Step 2: Substitute the given values.
\(R=4\) cm, \(r=3\) cm, \(h=10\) cm:
\[ V=\pi \times 10 \times (4^2-3^2) = 10\pi \times (16-9) = 10\pi \times 7 = 70\pi\ \text{cm}^3. \]
Step 3: Evaluate.
Using \(\pi=\dfrac{22}{7}\): \(V=70\times \dfrac{22}{7}=220\ \text{cm}^3.\)