Question

The length of a cylindrical metallic pipe is 14 cm. The difference between its outside and inside surface areas is $44c{m}^2$. Find the outer and inner radius of the pipe, if the pipe is made up of $110c{m}^3$ of metal.

Answer 1

Let r and R be the inner and outer radius of the cylindrical metallic piper respectively.
H be the height of the metallic pipe =14 cm
Difference between the Curved surface area of the outer cylinder and Curved surface area of the inner cylinder $=2\pi Rh-2\pi rh$
Given that difference between the outside and inside curved surface area of cylinder is $44c{m}^2$
$\Rightarrow 2\times \pi \times h(R-r)=44$
$\Rightarrow \frac{44}{7}\times 14(R-r)=44$
$\Rightarrow R-r=\frac{1}{2}=0.5\dots \dots \left(1\right)$
Given the pipe is made up of 99 cubic cm of metal so that
Volume of cylindrical metallic pipe $=\pi R^{2}h-\pi r^{2}h$
$\Rightarrow \frac{22}{7}\times 14(R^2-r^2)=99c{m}^3$
$\Rightarrow 44\times (R^2-r^2)=99$
$\Rightarrow (R^2-r^2)=\frac{9}{4}=2.25$
$\Rightarrow (R+r)(R-r)=2.25$
$=(0.5\times (R+r\left)\right)=2.25$
$R+r=\frac{2.25}{0.5}=4.5$
$R+r=4.5\dots \dots \left(2\right)$
Adding (1) and (2) we get
$2R=4.5+0.5=5$
$\therefore R=2.5cm$ and $r=2cm$
$\therefore$ Outer side radius R = 2.5 cm and inner side radius r = 2 cm.