#### Question

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

#### Solution

We have to find the outer and inner radius of a hollow pipe.

Radius of inner pipe be(r_{1})

Radius of outer cylinder be (r_{2})

Length of the cylinder(h) = 14 cm

Difference between the outer and the inner surface area is 44 cm^{2}

So,

2πh(r_{2} - r_{1}) = 44

`2(22/7)(14)(r_2-r_1)=44`

So,

(r_{2} - r_{1)}=`1/2`…… (1)

So, volume of metal used is 99 cm^{3} , so,

`pih(r_2^2-r_1^2)=99`

`(22/7)(14)(r_2-r_1)(r_2+r_1)=99`

Use equation (1) in the above to get,

`(22/7)(14)(1/2)(r_2+r_1)=99`

Therefore,

`(r_2+r_1)=9/2`…… (2)

Solve equation (1) and (2) to get,

`r_2=5/2cm`

`r_1=2cm`