It costs ₹ 3300 to paint the inner curved surface of a cylindrical v

1.	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» (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

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»

(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