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A day full of math games & activities. Find one near you.

It costs ₹ 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of ₹ 20 per m2, find
(i) inner curved surface area of the vessel,
(ii) radius of the base,
(iii) capacity of the vessel.

Solution:

Since the cost to paint the inner curved surface and its rate is known, we can obtain the inner CSA.

The ratio between the total cost and the rate per m2 will give the inner CSA in m2. 

CSA of a cylinder of base radius r, and height h = 2πrh

The volume of a cylinder of base radius r, and height h = π r2h

Total cost to paint inner CSA = ₹ 2200

Rate of painting = ₹ 20 per m2

Inner CSA of the cylindrical vessel = 2200/20 = 110 m2

Height of the vessel, h = 10m

Inner CSA of the vessel = 110 m2

2πrh = 110 m2

r = 110 / 2πh

= 110 /(2 × 10) × 7/22

= 7/4 m

= 1.75 m

Volume of the vessel = πr2h

= 22/7 × 1.75 m × 1.75 m × 10 m

= 96.25 m3

Thus, inner curved surface area is 110 m2, radius of the base is 1.75 m and capacity of the vessel is 96.25 m3.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

Video Solution:

It costs ₹ 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of ₹ 20 per m², find (i) inner curved surface area of the vessel, (ii) radius of the base, (iii) capacity of the vessel

NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.6 Question 5

Summary:

It is given that it costs ₹ 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. We have found that the inner curved surface area of the vessel is 110 m2 , the radius of the base is 1.75 m and capacity of the vessel is 96.25 m3.

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