# 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 m^{2}, 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 m^{2} will give the inner CSA in m^{2}.

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 r^{2}h

Total cost to paint inner CSA = ₹ 2200

Rate of painting = ₹ 20 per m^{2}

Inner CSA of the cylindrical vessel = 2200/20 = 110 m^{2}

Height of the vessel, h = 10m

Inner CSA of the vessel = 110 m^{2}

2πrh = 110 m^{2}

r = 110 / 2πh

= 110 /(2 × 10) × 7/22

= 7/4 m

= 1.75 m

Volume of the vessel = πr^{2}h

= 22/7 × 1.75 m × 1.75 m × 10 m

= 96.25 m^{3}

Thus, inner curved surface area is 110 m^{2}, radius of the base is 1.75 m and capacity of the vessel is 96.25 m^{3}.

**☛ 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 m^{2} , the radius of the base is 1.75 m and capacity of the vessel is 96.25 m^{3}.

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