Pavan built a conical flask using 550 m2 of aluminium sheet. If the

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Pavan built a conical flask using 550 $m^{2}$ of aluminium sheet. If the radius of the flask is 7 m, then how much water can be filled in the flask(in litres)? [The bottom of the flask is of another material.]

Options:

A . 1232 litres

B . 1232000 litres

C . 12300 litres

D . 123 litres

Answer: Option B
:
B

The area of aluminium sheet = Curved surface area of flask
$\Rightarrow 550 m^{2} = π r l$
$\Rightarrow 550 = \frac{22}{7} \times 7 \times l$
$\Rightarrow 550 = 22 l$
$\Rightarrow l = 25 m$

Now, height of flask
$\Rightarrow h = \sqrt{(l^{2} - r^{2})}$
$\Rightarrow h = \sqrt{25^{2} - 7^{2}}$
$\Rightarrow h = 24 m$

Hence, the volume of conical flask
$= \frac{1}{3}$ $π$ $r^{2} h$
$= \frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 24$
$= 1232 m^{3}$

We know that 1 m $^{3} = 1000 l i t r e s$

So, volume in litres $= 1232000 l i t r e s$

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