# The length of a metallic tube is 1 metre, its thickness is 1 cm and its inner diameter is 12 cm.

Question:

The length of a metallic tube is 1 metre, its thickness is 1 cm and its inner diameter is 12 cm. Find the weight of the tube if the density of the metal is 7.7 grams per cubic centimetre.

Solution:

Length $=1 \mathrm{~m}=100 \mathrm{~cm}$

Inner diameter $=12 \mathrm{~cm}$

Radius $=6 \mathrm{~cm}$

Now, inner volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\frac{22}{7} \times 6 \times 6 \times 100=11314.286 \mathrm{~cm}^{3}$

Thickness $=1 \mathrm{~cm}$

Total radius $=7 \mathrm{~cm}$

Now, we have the following:

Total volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\frac{22}{7} \times 7 \times 7 \times 100=15400 \mathrm{~cm}^{3}$

Volume of the tube $=$ total volume $-$ inner volume $=15400-11314.286=4085.714 \mathrm{~cm}^{3}$

Density of the tube $=7.7 \mathrm{~g} / \mathrm{cm}^{3}$

$\therefore$ Weight of the tube $=$ volume $\times$ density $=4085.714 \times 7.7=31459.9978 \mathrm{~g}=31.459 \mathrm{~kg}$