Question

The sum of the both curved surface of a hollow metallic cylinder is $1408$ $c{m}^2$ and the volume of metal in it is $1408$ $c{m}^3$. Find the thickness of the metal in this cylinder if its height is $28$ cm.

Answer 1

Let us take outer radius $=R$, inner radius $=r$
Height $=28$ cm
Sum of both the curved surfaces of a hollow metallic cylinder $=1408$ $c{m}^2$
$\Rightarrow 2\pi Rh+2\pi rh=1408$

$\Rightarrow 2\pi h(R+r)=1408$
$\Rightarrow (R+r)=\frac{1408\times 7}{28\times 2\times 22}$
$\Rightarrow (R+r)=8$ .........(1)
Volume of metal $=1408$ $c{m}^3$
$\Rightarrow \pi R^{2}h-\pi r^{2}h=1408$
$\Rightarrow R^2-r^2=\left(\frac{1408}{28}\right)÷\left(\frac{22}{7}\right)$
$\Rightarrow (R+r)(R-r)=\frac{1408\times 7}{28\times 22}$
$\Rightarrow (R+r)(R-r)=16$

After taking the value of $(R+r)$ from (1),

$\Rightarrow 8\times (R-r)=16$
$\Rightarrow (R-r)=2$
Thickness of the metal in this cylinder $=2$ cm