Question

13) A 4.2 m long iron pipe with internal
diameter of 10 cm is 1 cm thick. Find
the volume of the iron in the pipe. If
1 cmof iron weighs 8 g, find the total
weight of iron in the pipe.

ans is 14,520 cu cm​

Answer 1

Given:

The iron pipe is 4.2 m long.

It has a internal diameter of 10 cm.

The iron used is 1 cm thick.

1 cm³ of iron weighs 8g.

To Find:

The weight of the iron pipe.

Formula Used:

$\text{Volume } = \pi r^2 h$

Solution

Find the external volume of the pipe:

$\text{External Radius } = \text{Diameter} \div 2 + \text{thickness of the iron}$

$\text{External Radius } = (10 \div 2) + 1$

$\text{External Radius } = 6 \text { m}$

$\text{Volume } = \pi r^2 h$

$\text{Volume } = \pi (6)^2 (420)$

$\text{Volume } = 15120 \pi \text { cm}^2$

Find the interior volume of the pipe:

$\text{Interior Radius } = 10 \div 2$

$\text{External Radius } = 5 \text { m}$

$\text{Volume } = \pi r^2 h$

$\text{Volume } = \pi (5)^2 (420)$

$\text{Volume } = 10500\pi \text { cm}^2$

Find the volume of the iron used:

$\text{Volume of the iron used} = 15120\pi - 10500\pi$

$\text{Volume of the iron used } = 4620\pi \text { cm}^2$

$\text{Volume of the iron used } = 14520 \text { cm}^2$

Find the weight of the iron used:

$\text{Weight of the iron used } = 14520 \times 8$

$\text{Weight of the iron used } = 116160 \text{ g}$

$\text{Weight of the iron used } = 116.16 \text { kg}$

Answer: 116.16 kg