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It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m2, find - CBSE Class 9 - Mathematics

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Question

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

(i) Inner curved surface area of the vessel

(ii) Radius of the base

(iii) Capacity of the vessel

`["Assume "pi=22/7]`

 

Solution

(i) Rs 20 is the cost of painting 1 m2 area.

`"Rs. 2200 is the cost of painting "=(1/20xx2200)m^2" area"`

= 110 m2 area

Therefore, the inner surface area of the vessel is 110 m2.

 

(ii) Let the radius of the base of the vessel be r.

Height (h) of vessel = 10 m

Surface area = 2πrh = 110 m2

`rArr(2xx22/7xxr xx10)m = 110m^2`

`rArr r=(7/4)m = 1.75m`

 

(iii) Volume of vessel = πr2h

`=[22/7xx(1.75)^2xx10]m^3`

= 96.25 m3

Therefore, the capacity of the vessel is 96.25 m3 or 96250 litres.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 13: Surface Area and Volumes
Ex. 13.60 | Q: 5 | Page no. 231

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Solution It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m2, find Concept: Volume of a Cylinder.
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