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# It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel $ 10 \mathrm{~m} $ decp. If the cost of painting is at the rate of $ Rs. 20 $ per $ \mathrm{m}^{2} $, find

**(i)** inner curved surface area of the vessel,

**(ii)** radius of the base,

**(iii)** capacity of the vessel.

**Given:**

It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel \( 10 \mathrm{~m} \) decp.

The cost of painting is at the rate of \( Rs. 20 \) per \( \mathrm{m}^{2} \).

To do:

We have to find

(i) inner curved surface area of the vessel

(ii) radius of the base

(iii) capacity of the vessel.

**Solution:**

(i) The cost to paint the inner curved surface of the cylindrical vessel $= Rs.\ 2200$

Cost of painting per $m^2 = Rs.\ 20$

This implies,

Inner curved surface area of the cylindrical vessel $=\frac{\text { Cost to paint the inner curved surface }}{\text { Cost of painting per } \mathrm{m}^{2}}$

Therefore,

$2 \pi r h=\frac{Rs.\ 2200}{Rs.\ 20}$

$2 \pi rh=110 \mathrm{~m}^{2}$

The inner curved surface area of the vessel is $110\ m^2$.

(ii) $2 \times \frac{22}{7} \times r \times 10 =110$

$r=\frac{110 \times 7}{2 \times 22 \times 10}$

$r=\frac{7}{4}$

$r=1.75 \mathrm{~m}$

Hence, the radius of the base is $1.75\ m$.

(iii) Capacity of the vessel $=$ Volume of the vessel

$=\pi r^{2} h$

$=\frac{22}{7} \times (\frac{7}{4})^2 \times 10$

$=\frac{77}{8}$

$=96.25 \mathrm{~m}^{3}$

Hence, the capacity of the vessel is $96.25\ m^3$.

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