Question

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

Answer 1

(i) We know that

Cost of painting inner curved surface of the vessel = cost of painting per m² × inner curved surface of vessel

By substituting the values

3300 = 30 × Inner curved surface of vessel

On further calculation

Inner curved surface of vessel = 110 m²

(ii) Consider r as the inner radius of the base

It is given that depth = 10m

We know that

Inner curved surface of vessel = 2 πrh

By substituting the values

110 = 2 × (22/7) × r × 10

So we get

r = (110 × 7)/ (2 × 22 × 10)

r = 1.75m

(iii) We know that

Capacity of the vessel = πr²h

By substituting the values

Capacity of the vessel = (22/7) × (1.75)² × 10

So we get

Capacity of the vessel = 96.25 m³