# 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 - Mathematics

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

(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.

Concept: Volume of a Cylinder
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Chapter 13: Surface Area and Volumes - Exercise 13.6 [Page 231]

#### APPEARS IN

NCERT Class 9 Maths
Chapter 13 Surface Area and Volumes
Exercise 13.6 | Q 5 | Page 231

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