A construction company purchased a big cylindrical vessel to keep… - Vidyadip

Question

A construction company purchased a big cylindrical vessel to keep some liquid on it. Before using this vessel, the company decided to paint it properly. It costed $₹\ 3300$ to paint the inner curved surface of this $10 \ m$ deep cylindrical vessel at the rate of $₹\ 30$ per $m^2$.

$i.$ Find the inner curved surface area of the vessel,
$ii.$ Find the inner radius of the base and capacity of the vessel.

✓

Answer

$i.$ cost of painting inner curved surface area of vessel
$=$ cost of painting per $m^2 \times$ Inner curved surface of vessel
$\Rightarrow ₹\ 3300= ₹\ 30\ \times$ Inner curved surface of vessel
$\Rightarrow$ Inner curved surface of vessel $=110 m^2$
$ii.$ Let inner radius of the base $= r$
Depth, $h = 10\ m$
Inner curved surface of vessel $=2 \pi h$
$\Rightarrow 110=2 \times \frac{22}{7} \times r \times 10$
$\Rightarrow r=\frac{110 \times 7}{2 \times 22 \times 10}=1.75 m$
$iii$. Capacity of the vessel $=\pi r^2 h$
$=\left(\frac{22}{7} \times 1.75 \times 1.75 \times 10\right) m ^3$
$=96.25 m^3$

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