It costs ₹ 3300 to paint the inner curved surface of a cylindrical vessel 10 m deep at the rate of Rs 30 per m2. Find the

Total cost of paining the inner curved surface of the cylinderical vassel = ₹ 3,300

Rate of painting = ₹ 30 per m2

(i) Inner curved surface area of the vassel

$=\frac{\text { Total cost of painting the inner curved surface of the cylindrical vassel }}{\text { Rate of painting }}$

$=\frac{3300}{30}$

$=110 \mathrm{~m}^{2}$

Thus, the inner curved surface area of the vassel is 110 m2.

(ii) Depth of the vassel, h = 10 m

Let the inner radius of the base be r m.

$\therefore$ Inner curved surface area of the vasssel $=2 \pi r h=2 \times \frac{22}{7} \times r \times 10$

$\Rightarrow 2 \times \frac{22}{7} \times r \times 10=110$

$\Rightarrow r=\frac{110 \times 7}{2 \times 22 \times 10}$

$\Rightarrow r=1.75 \mathrm{~m}$

Thus, the inner radius of the base is 1.75 m.

(iii) Capacity of the vassel $=\pi r^{2} h=\frac{22}{7} \times(1.75)^{2} \times 10=96.25 \mathrm{~m}^{3}$

Thus, the capacity of the vassel is 96.25 m3.