Question

The capacity of a closed cylindrical vessel of height $1m$ is $15.4litres$. How many square metres of metal sheet would be needed to make it?

Answer 1

Capacity of vessel$=15.4l=0.0154m^3$

height of vessel$=1m$

let radios of cylindrical vessel be 'r' m.

Now, $\pi r^{2}h=0.0154$

$\frac{22}{7}\times r^2\times 1=0.0154r^2=\frac{0.0154\times 7}{22}=0.0007\times 7$

$r^2=0.0049$

$r=0.07m$

curved surface area$=2\pi rh=2\times \frac{22}{7}\times 0.07\times 1=0.44m^2$

Now, total surface area of the vessel $=2\pi r(r+h)$

$=2\times \frac{22}{7}\times 0.07(0.07+1)=0.47m^2$

Hence, $0.47$ square metres of metal sheet would be needed to make the cylindrical vessel.