 # A cylindrical vessel, without lid, has to be tin-coated on its both sides.

Question:

A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 3.50 per 1000 cm2.

Solution:

Let $r \mathrm{~cm}$ and $h \mathrm{~cm}$ be the radius of the cylindrical vessel.

Given :

Radius, $r=70 \mathrm{~cm}$

Height, $h=1.4 \mathrm{~m}=140 \mathrm{~cm}$

Rate of tin $-$ plating $=$ Rs $3.50$ per 1000 square centimetre

Cost of tin - plating the cylindrical vessel on both the surfaces (inner and outer):

Total suface area of a vessel = Area of the inner and the outer side of the base + Area of the inner and the outer curved surface

$=2\left(\pi r^{2}+2 \pi r h\right)$

$=2 \pi r(\mathrm{r}+2 h)$

$=2 \times \frac{22}{7} \times 70 \times(70+2 \times 140)$

$=44 \times 10 \times 350$

$=154000 \mathrm{~cm}^{2}$

Cost of painting at the rate of Rs $3.50$ per $1000 \mathrm{~cm}^{2}=154000 \times \frac{3.50}{1000}=$ Rs 539

Therefore, cost of painting is Rs 539 .