Question

The diagram has a hollow cylindrical tube, of internal radius 4cm and external radius 6cm. How can I determine the area of an external curved surface, how can I get the area of the inner curved surface and how can I get the total surface area of the tube?

Answer 1

Given:

internal radius = 4cm

External radius = 6cm

Height = 20cm

Curved surface area of the external surface

The formula for the curved surface is:

`\begin{gathered} =2\pi rh \\ \text{Where r is a radius} \\ \text{and h is the height of the cylinder} \end{gathered}`

Hence, the curved surface area:

`\begin{gathered} C\mathrm{}S\mathrm{}A\text{ of external surface = 2}*\pi*6*20 \\ =753.982cm^2 \end{gathered}`

Curved surface area of the inner surface:

`\begin{gathered} C\mathrm{}S\mathrm{}A\text{ of inner surface = 2 }*\pi*4*\text{ 20} \\ =502.654cm^2 \end{gathered}`

The total surface area of the tube :

The total surface area can be found using the formula:

`\text{Total Surface area = }2\pi(R^2-r^2)\text{ + }2\pi h(R\text{ + r)}`

Where R is the radius of the external surface and r is the radius of the inner surface

Hence:

`\begin{gathered} \text{Total Surface area = 2}*\pi*(6^2-4^2)\text{ + 2}*\pi*20*(6\text{ + 4)} \\ =\text{ }1382.3cm^2 \end{gathered}`