Question

The difference between outside and inside surface areas of cylindrical metallic pipe of 14 cm long is 44 $c{m}^2$. If the pipe is made of 99 $c{m}^3$ of metal, find the outer and inner radii of the pipe.

Answer 1

Hint: Here we will find the radii of outer and inner radii of pipe using the area and volume of cylindrical formula.

Complete step-by-step answer:
Let inner and outer radii of the cylindrical pipe be r and R respectively and height h=14 cm.
The difference between outside and inside surface area of cylindrical metallic pipe is
$$\begin{gathered} 2\pi (R-r)\times h=44\Rightarrow R-r={\displaystyle \frac{44\times 7}{44\times 14}}=0.5 \\ \Rightarrow R-r=0.5\to (1) \end{gathered}$$
Volume of pipe is
$$\begin{gathered} \Rightarrow \pi (R^2-r^2)\times h=99 \\ \Rightarrow R^2-r^2={\displaystyle \frac{99\times 7}{22\times 14}}=2.25 \\ \Rightarrow (R+r)(R-r)=2.25\Rightarrow 0.5\times (R+r)=2.25 \\ \Rightarrow R+r=4.5\to (2) \end{gathered}$$
Adding (1) and (2) we get
$$\begin{gathered} R-r=0.5 \\ R+r=4.5 \\ 2R=5\Rightarrow R=2.5 \end{gathered}$$
Put value of R into equation (2) to get value of r
$r=4.5-2.5=2$
The value of inner(r) and outer (R) radii are 2cm and 2.5 cm respectively.

Note: By applying the formula of surface area and volume of cylinder, we can easily solve questions. Mistakes can be avoided in the assignment of units.