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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 $${m}^2$$, findi) inner curved surface area of the vessel,ii) radius of the base,iii) capacity of the vessel.

i)Given :
Rs. 20 is the cost Of painting 1 $${m}^2$$ area.
$$\therefore$$ when Rs. 2200 is the cost of painting, area is
= $$\frac{1}{20} × 2200$$ $${m}^2$$
= 110 $${m}^2$$ area

Therefore, the inner curved surface area of the vessel is 110 $${m}^2$$.

ii)Height (h) of vessel = 10 m
Surface area = 110 $${m}^2$$

Let the radius of the base of the vessel be r.

We know that,

Surface area = $$2 {\pi} r h$$

But, CSA = 110 $${m}^2$$ ...(from i))
$$\Rightarrow$$ 110 $${m}^2$$ = $$2 × \frac{22}{7} × r × 10 m$$
$$\Rightarrow$$ r = $$\frac{7}{4} m = 1.75 m$$

iii) Now, volume of vessel
= $${\pi} {r}^2 h$$
= $$22 × (1.75)^2 × 10 {m}^3$$
= 96.25 $${m}^3$$

Therefore, the capacity of the vessel is 96.25 $${m}^3$$ or 96250 litres.