Question

It costs Rs 2200 to paint the inner curved surface of a cylinderical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m2, find: (i) radius of the base (ii) inner curved surface area of the vessel (iii)capacity of the vessel (in litres).

Answer 1

1)110m^2

2)1.75m

3)96.25m^2

Explanation:

Rate of painting= The cost to paint it /

inner curved surface area of the vessel

20m^2=(Rs 2200 /inner curved surface area of the vessel)

If we make inner curved surface area of the vessel subject of the formula,

inner curved surface area of the vessel= =(Rs 2200/20)

= 110m^2

2)cost surface area of a cylinder can be calculated using expression below

(2πrh,) then the values was calculated in question 1 as 110m^2

Then from (2πrh=110) we can make "r" subject of the formula

r= 110/(2πh). h=10m deep

r=110/(2×3.14×10)

r= 1.75m

3)(iii)capacity of the vessel (in litres

The capacity of the vessel can be regarded as the volume which equals to πr^2h

From question 2 r=1.75m, and h=10m

Then

πr^2h= 3.142×(1.75)^2 ×10

=96.25m^2

Hence the capacity is 96.25m^2