Question

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It costs Rs.2200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the cost of painting is at the rate of Rs.20 per m2. Find

1. inner curved surface area of vessel.
2. Radius of base.
3. Capacity of vessel.


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Answer 1

Answer:

96.25m^3

Step-by-step explanation:

Total cost of point=2200Rs.

Cost of point/m ^2 =20Rs.

Depth of vessel=10m

Inner curved surface area painted= 2200/20=110m^2

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Now, 2πrh=110m ^2

Or, 2×22/7×r×10=110

or, r=1.75m

Radius of the base is 1.75m.

Capacity of vessel

=πr ^2h

=22/7×1.75×1.75×10

=96.25m^3

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Answer 2

Given :-

Cost of painting 1 per m^2 = Rs.20

Cost of painting = 2200

Height of the cylindrical vessel = 10m

Solution 1 :-

Let the inner CSA be x

Cost of painting 1 per m^2 = Rs 20

Therefore ,

Cost of painting

= Inner CSA * Rate of painting

2200 = x * 20

x = 2200/20

x = 110

Hence , The inner surface area of cylindrical vessel is 110 m^2

Solution 2 :-

Now ,

We know the CSA of cylinder = 110m^2

Let the radius of cylinder be r

Height of cylinder = 10m

2πrh = 110

2 * 22/7 * r * 10 = 110

r = 110 * 7 / 2 * 22 * 10

r = 7/4

Hence , The radius of the cylinder

= 7/4m or 1.75 m

Solution 3 :-

Here ,

Radius of cylinder = 7/4 m

Height of cylinder = 10 m

Now , We have to find capacity of the vessel =?

Volume of cylinder = πr^2h

Volume of cylinder = 22/7 * 7/4 * 7/4 * 10

Volume of cylinder = 11 * 7/4 * 5

Volume of the cylinder

= 96.25 m^2$.$