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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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