To show that the area of the cross-section of the pipe is $1.84\pi$ cm², we need to calculate the area of the annular (ring-shaped) cross-section formed between the external and internal surfaces of the pipe.

Given Data:

• External radius ($R$): 2.5 cm
• Internal radius ($r$): 2.1 cm

Step-by-Step Calculation:

1. Area of the external circle: $\text{Area}_{\text{external}} = \pi R^2 = \pi (2.5)^2 = \pi \times 6.25 \text{ cm}^2$

2. Area of the internal circle: $\text{Area}_{\text{internal}} = \pi r^2 = \pi (2.1)^2 = \pi \times 4.41 \text{ cm}^2$

3. Area of the cross-section:

   = \pi \times 6.25 - \pi \times 4.41 = \pi \times (6.25 - 4.41) = \pi \times 1.84 \text{ cm}^2$$

Thus, the area of the cross-section is indeed $1.84\pi$ cm², as required.

Would you like further details or have any other questions?

Relative Questions:

1. What is the formula for the area of a circle?
2. How do you calculate the area of an annulus (ring)?
3. What does the cross-sectional area represent in this context?
4. How would the area change if the pipe's thickness increased?
5. Why is the difference between the squares of the radii taken?
6. How does the cross-sectional area relate to the volume of the pipe?
7. What happens to the cross-sectional area if both radii are doubled?
8. How would you calculate the cross-sectional area if the pipe were hollow with a square cross-section?

Tip:

When working with circles and annuli, always double-check the radii and ensure you subtract the areas correctly to avoid common mistakes.