Question

The thickness of a metallic tube is 1cm and the inner diameter of the tube is 12 cm. Find the weight of 1 m long tube, if the density of the metal be 7.8 g/cm³.

Answer 1

The weight of the 1 m long tube is approximately $31.85\,\text{kg}$.

Answer 2

Solution:

1. Determine the radii:

   • Inner radius, $r_i = \frac{12}{2} = 6$ cm.
   • Outer radius, $r_o = 6 + 1 = 7$ cm (since thickness = 1 cm).

2. Calculate cross-sectional area of the tube:

   $$A = \pi \left(r_o^2 - r_i^2\right) = \pi \left(7^2 - 6^2\right) = \pi (49 - 36) = 13\pi \, \text{cm}^2.$$

3. Find the volume:

   • Convert the tube length to centimeters: $1\,\text{m} = 100\,\text{cm}$.
   $$V = A \times \text{length} = 13\pi \times 100 = 1300\pi \, \text{cm}^3.$$

4. Compute the weight (mass) using density:

   $$\text{Mass} = \text{density} \times V = 7.8\,\text{g/cm}^3 \times 1300\pi\,\text{cm}^3 = 10140\pi\,\text{g}.$$

   Approximating:

   $$10140\pi \approx 10140 \times 3.1416 \approx 31854\,\text{g} \approx 31.85\,\text{kg}.$$

Core Explanation:

• Use inner radius $6$ cm; add thickness to get outer radius $7$ cm.
• Compute area: $\pi(7^2-6^2)=13\pi$ cm².
• Volume = $13\pi \times 100=1300\pi$ cm³.
• Mass = density $\times$ volume = $7.8 \times 1300\pi = 10140\pi$ g ≈ 31.85 kg.