Question

The outer diameter of a metallic pipe is 18 cm and the thickness of the pipe is 2 cm and the height is 4 cm. Find the surface area of the metallic pipe.

Answer 1

Hint: The curved surface area of a cylinder is $2\pi rh$, where r = radius of the cylinder and h = height of the cylinder and value of $\pi ={\displaystyle \frac{22}{7}}$.
Another important trick is
Outer diameter=inner diameter+2 times thickness of the pipe

Complete step-by-step answer:

As mentioned in the question, we need to find the complete surface area or total surface area of the metallic pipe.
For finding the total surface area or the complete surface area, we need to add the surface area of the outer surface as well as the inner surface of the metallic pipe.
Using the trick mentioned in the hint, as the outer diameter of the metallic pipe is given as 18cm, so, the inner diameter of the metallic pipe is
Outer diameter=inner diameter+2 times thickness of the pipe
18=inner diameter + $$2\times 2$$
(18-4)cm=inner diameter
Inner diameter =14cm
Now, we have both inner and outer diameters of the metallic pipe, so , we can find the outer radius as well as the inner radius of the metallic pipe as
Diameter =2 times the radius
So,
Outer radius $$={\displaystyle \frac{outerdiameter}{2}}$$ and the inner radius $$={\displaystyle \frac{innerdiameter}{2}}$$ .
Therefore, the outer radius is 9cm and the inner radius is 7cm.
Now, the total surface area = outer curved surface area + inner curved surface area +area of the two ends
Now, using the formula, we get
outer curved surface area is
$$\begin{array}{rl}& =2\pi 9h\\ & =2\times 3.14\times 9\times 4\\ & =226.08c{m}^2\end{array}$$
Similarly, inner curved surface area is
$$\begin{array}{rl}& =2\pi 7h\\ & =2\times 3.14\times 7\times 4\\ & =175.84c{m}^2\end{array}$$
And the area of the two ends is
$$\begin{array}{rl}& =\pi {(outerradius)}^2-\pi {(innerradius)}^2\\ & =\pi {(9)}^2-\pi {(7)}^2\\ & =100.48c{m}^2\end{array}$$
Hence, the total surface area
$$\begin{array}{rl}& =226.08+175.84+100.48\\ & =502.40c{m}^2\end{array}$$

Note: The students can make an error in including the two circular ends of the metallic pipe while evaluating the complete surface area or the total surface area of the metallic pipe. Neglecting those two rings in the total area can lead the student in a wrong direction.