Question

Pavan built a conical flask using $550m^2$ of aluminium sheet. If the radius of the flask is $7m,$ then how much water can he fill into the flask (in litres)?
(The bottom of flask was made out of some other material.)

• A. $1232l$
• B. $1232000l$
• C. $123200l$
• D. $1.232l$

Answer 1

The correct option is B

$1232000l$

Let 'r', 'h' and 'l' be the radius, height and slant height of the conical flask respectively.
Note that,
the area of aluminium sheet = Curved surface area of the flask

$\Rightarrow 550m^2=\pi rl$

$\Rightarrow 550m^2=\frac{22}{7}\times 7\times l$

$\Rightarrow l=25m$

Then, $h=\sqrt{(l^2-r^2)}$

$\Rightarrow h=\sqrt{{25}^2-7^2}$

$\Rightarrow h=24m$

Volume of conical flask

$=\frac{1}{3}$ $\pi$$r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24$

$=1232m^3$

We know that $1m^3=1000l$

So, volume in litres $=1232000l$

Therefore, Pavan can fill 1232000 litres of water into the conical flask.