Question

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

Answer 1

Let inner and outer radii of the cylindrical pipe be r and R respectively and height, h $=$ 14cm. Then,

$2\pi (R-r)h=44\Rightarrow R-r=\frac{44\times 7}{44\times 14}=0.5⟶\left(1\right)$

Volume of pipe $=\pi (R^2-r^2)h=99{cm}^3\Rightarrow R^2-r^2=\frac{99\times 7}{22\times 14}=2.25$

$\Rightarrow (R-r)(R+r)=2.25\Rightarrow 0.5(R+r)=2.25{\left[from\right(1\left)\right]}^2$

$\Rightarrow R+r=4.5⟶\left(2\right)$

Adding (1) and (2), we get, $2R=5\Rightarrow R=2.5\&r=2cm$