It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m², find

(I) Cost of painting the inner curved surface of cylindrical vessel = Rs 2200 and height h = 10 m.
Let, the inner radius of cylindrical vessel = r m
The inner curved surface area of cylindrical vessel = 2πrh
The cost of painting is at the rate of Rs 20 per m² = Rs 20 × 2πrh
According to question, Rs 20 × 2πrh = 2200
⇒ 2πrh = 2200/20 = 110
Hence, the inner curved surface area is 110 m².

(II) The inner curved surface area of cylindrical vessel = 2πrh
⇒ 110 = 2 × 22/7 × r × 10 ⇒ r = 110×7/22×2×10 = 7/4 = 1.75 m
Hence, the radius of base of cylindrical vessel is 1.75 m.

(III) Volume of cylindrical cessel = πr²h
= 22/7 × 1.75 × 1.75 × 10 = 22 × 0.25 × 1.75 × 10 = 96.25 m³
Hence, the volume of cylindrical vessel is 96.25 m³.