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
Question:

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
(i) inner curved surface area of the vessel,
(ii) inner radius of the base, and
(iii) capacity of the vessel.

Solution:

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.