The outer and inner diameters

The outer and inner diameters of a hollow cylindrical pipe are 10 cm and 6 cm respectively. The length of the pipe is 21 cm. We want to find its total surface area (TSA).

Step 1: Determine radii
The outer radius is $R = \frac{10}{2} = 5 , \text{cm}$ and the inner radius is $r = \frac{6}{2} = 3 , \text{cm}$. The height of the cylinder is $h = 21 , \text{cm}$.

Step 2: Formula for Total Surface Area
The total surface area of a hollow cylinder is given by:
$ \text{TSA} = 2 \pi R h + 2 \pi r h + 2 \pi (R^2 - r^2) $

Step 3: Substitute the values
$ \text{TSA} = 2 \pi (5)(21) + 2 \pi (3)(21) + 2 \pi (5^2 - 3^2) $
$ \text{TSA} = 210 \pi + 126 \pi + 32 \pi $
$ \text{TSA} = 368 \pi , \text{cm}^2 $

Step 4: Approximate value
$ \text{TSA} \approx 368 \times 3.1416 \approx 1156.8 , \text{cm}^2 $

Answer:
$ \text{TSA} = 368 \pi , \text{cm}^2 $