A cylinder pipe, made of metal is 3cm thick.If the internal radius of the pipe is 10cm.Find the volume of metal used in making 3m of the pipe.

1. Analyze the question

We are asked to find the volume of metal used to make a cylindrical pipe.

• Internal radius ($r$): 10 cm
• Thickness of the pipe: 3 cm
• Length (height, $h$) of the pipe: 3 m
• Goal: Calculate the volume of the metal (the hollow part).

2. Explain the concept

A cylindrical pipe is essentially a hollow cylinder. The volume of the metal used is the difference between the outer cylinder and the inner cylinder.

• Internal radius ($r$): 10 cm
• External radius ($R$): Internal radius + Thickness = $10\text{ cm} + 3\text{ cm} = 13\text{ cm}$
• Height ($h$): Since the radii are in cm, we must convert the length to cm. $3\text{ m} = 300\text{ cm}$.
• Formula for Volume of a hollow cylinder: $V = \pi h(R^2 - r^2)$

3. Show the solution

Step 1: Identify the dimensions

• $R = 13\text{ cm}$
• $r = 10\text{ cm}$
• $h = 300\text{ cm}$

Step 2: Apply the formula $V = \pi \times h \times (R^2 - r^2)$ $V = \pi \times 300 \times (13^2 - 10^2)$

Step 3: Calculate the squares $13^2 = 169$ $10^2 = 100$

Step 4: Subtract and multiply $V = \pi \times 300 \times (169 - 100)$ $V = \pi \times 300 \times 69$ $V = 20,700\pi\text{ cm}^3$

4. Identify the answer

Comparing our result to the given options: A. $153\pi\text{ cm}^3$ B. $207\pi\text{ cm}^3$ C. $15,300\pi\text{ cm}^3$ D. $20,700\pi\text{ cm}^3$

The correct option is D.

5. Tip

Always check your units before calculating! In JAMB questions, they often mix meters and centimeters to test if you remember to convert them to the same unit. If you had used $h = 3$ instead of $300$, you would have gotten $207\pi$, which is option B—a common "distractor" answer designed to catch students who forget to convert units.