The height of a circular cyclinder is 20 cm and the diamete rof its bases is 4cm . Find :
its volume
(ii) its total surface area

Answer

To solve the problem, we will find the volume and total surface area of a circular cylinder given its height and diameter.

### Given:
- Height (h) = 20 cm
- Diameter (d) = 4 cm

### Step 1: Find the radius of the cylinder
The radius (r) can be calculated from the diameter using the formula:
\[ r = \frac{d}{2} \]

Substituting the given diameter:
\[ r = \frac{4 \, \text{cm}}{2} = 2 \, \text{cm} \]

### Step 2: Calculate the volume of the cylinder
The formula for the volume (V) of a cylinder is:
\[ V = \pi r^2 h \]

Substituting the values of \( r \) and \( h \):
\[ V = \pi (2 \, \text{cm})^2 (20 \, \text{cm}) \]
\[ V = \pi (4 \, \text{cm}^2) (20 \, \text{cm}) \]
\[ V = 80\pi \, \text{cm}^3 \]

Using \( \pi \approx \frac{22}{7} \):
\[ V \approx 80 \times \frac{22}{7} \]
\[ V \approx \frac{1760}{7} \]
\[ V \approx 251.43 \, \text{cm}^3 \]

### Step 3: Calculate the total surface area of the cylinder
The formula for the total surface area (A) of a cylinder is:
\[ A = 2\pi r (r + h) \]

Substituting the values of \( r \) and \( h \):
\[ A = 2\pi (2 \, \text{cm}) (2 \, \text{cm} + 20 \, \text{cm}) \]
\[ A = 2\pi (2 \, \text{cm}) (22 \, \text{cm}) \]
\[ A = 88\pi \, \text{cm}^2 \]

Using \( \pi \approx \frac{22}{7} \):
\[ A \approx 88 \times \frac{22}{7} \]
\[ A \approx \frac{1936}{7} \]
\[ A \approx 276.57 \, \text{cm}^2 \]

### Final Answers:
1. Volume of the cylinder = \( 251.43 \, \text{cm}^3 \)
2. Total surface area of the cylinder = \( 276.57 \, \text{cm}^2 \)

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