Question

"Question 5 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 m^2 , find (i) Inner curved surface area of the vessel (ii) Radius of the base (iii) Capacity of the vessel

Class 9 - Math - Surface Areas and Volumes Page 231"

Answer 1

(i) inner curved surface area = Rs 2200/20
                                                     = 110m2
(ii) radius of the base = 2 pie rh
                                     110=2*22/7*r*10                     
                                          r=1.75
(iii) capacity of the vessel= pie r2 h
                                             = 22/7* 1.752 *10 

                                             =96.25m3

Answer 2

Let r be the radius of a vessel.

Given: cost to paint the inner curved surface area= ₹2200

Cost to paint per m²= ₹20 & height of vessel (h)= 10 m

Curved surface area= 2πrh

Inner curved surface area=cost to paint the inner curved surface area/cost of paint per m²

2πrh= 2200/20= 110 m²

2× 22/7×r× 10= 110

 r=(110×7)/(2×220)= 7/4= 1.75m

i)

Inner curved surface area of the vessel= 110 m²

ii)

Radius of the base radius of the base= 1.75 m

iii) capacity of The vessel= volume of the vessel

=πr²h= 22/7×7/4×7/4×10= 96.25 m³

= 96.25× 1000 L= 96.25 kL

[ 1 m= 100cm,  1 m³= 100 cm³

1000 cm³= 1L, 1000L= 1kL]

 capacity of The vessel= 96.25 kL

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Hope this will help you....