Question

31. It costs ? 3300 to paint the inner curved surface of a cylindrical vessel
10 m deep at the rate of 30 per m. Find the
(i) inner curved surface area of the vessel.
(ii) inner radius of the base, and
(iii) capacity of the vessel.
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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 = 110m²

(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 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

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