**Question:**

A cylindrical vessel open at the top has diameter 20 cm and height 14 cm. Find the cost of tin-plating it on the inside at the rate of 50 paise per hundred square centimetre.

**Solution:**

Given:

Diameter, $d=20 \mathrm{~cm}$

Radius, $r=10 \mathrm{~cm}$

Height, $h=14 \mathrm{~cm}$

Area inside the cylindrical vessel that is to be tin $-$ plated $=S$

$S=2 \pi r h+\pi r^{2}$

$=2 \pi \times 10 \times 14+\pi \times 10^{2}$

$=280 \pi+100 \pi$

$=380 \times \frac{22}{7} \mathrm{~cm}^{2}$

$=\frac{8360}{7} \mathrm{~cm}^{2}$

According to question:

Cost per $100 \mathrm{~cm}^{2}=50$ paise

Cost per $\mathrm{cm}^{2}=\operatorname{Rs} 0.005$

Cost of tin - plating the area inside the cylindrical vessel $=R s 0.005 \times \frac{8360}{7}$

$=\operatorname{Rs} \frac{41.8}{7}=\operatorname{Rs} 5.97$