The base radius of a cylinder is 14 cm and its heights is 30 cm. Find :
(a) volume (b) curved surface area (c) total surface area

Answer

To solve the problem, we will calculate the volume, curved surface area, and total surface area of the cylinder step by step.

### Given:
- Base radius (r) = 14 cm
- Height (h) = 30 cm

### (a) Volume of the Cylinder
The formula for the volume (V) of a cylinder is given by:
\[ V = \pi r^2 h \]

1. Substitute the values into the formula:
\[ V = \frac{22}{7} \times (14)^2 \times 30 \]

2. Calculate \( (14)^2 \):
\[ (14)^2 = 196 \]

3. Now substitute back into the volume formula:
\[ V = \frac{22}{7} \times 196 \times 30 \]

4. Simplify \( \frac{196}{7} \):
\[ \frac{196}{7} = 28 \]

5. Now calculate:
\[ V = 22 \times 28 \times 30 \]

6. Calculate \( 22 \times 28 \):
\[ 22 \times 28 = 616 \]

7. Finally, calculate \( 616 \times 30 \):
\[ V = 616 \times 30 = 18480 \text{ cm}^3 \]

### (b) Curved Surface Area of the Cylinder
The formula for the curved surface area (CSA) of a cylinder is:
\[ CSA = 2 \pi r h \]

1. Substitute the values into the formula:
\[ CSA = 2 \times \frac{22}{7} \times 14 \times 30 \]

2. Calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]

3. Now substitute back into the CSA formula:
\[ CSA = \frac{44}{7} \times 14 \times 30 \]

4. Simplify \( \frac{44 \times 14}{7} \):
\[ \frac{44 \times 14}{7} = 88 \]

5. Now calculate:
\[ CSA = 88 \times 30 \]

6. Finally, calculate:
\[ CSA = 2640 \text{ cm}^2 \]

### (c) Total Surface Area of the Cylinder
The formula for the total surface area (TSA) of a cylinder is:
\[ TSA = 2 \pi r (r + h) \]

1. Substitute the values into the formula:
\[ TSA = 2 \times \frac{22}{7} \times 14 \times (14 + 30) \]

2. Calculate \( 14 + 30 \):
\[ 14 + 30 = 44 \]

3. Now substitute back into the TSA formula:
\[ TSA = 2 \times \frac{22}{7} \times 14 \times 44 \]

4. Simplify \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]

5. Now substitute back:
\[ TSA = \frac{44}{7} \times 14 \times 44 \]

6. Simplify \( \frac{44 \times 14}{7} \):
\[ \frac{44 \times 14}{7} = 88 \]

7. Now calculate:
\[ TSA = 88 \times 44 \]

8. Finally, calculate:
\[ TSA = 3872 \text{ cm}^2 \]

### Summary of Results:
- Volume of the cylinder = \( 18480 \text{ cm}^3 \)
- Curved Surface Area = \( 2640 \text{ cm}^2 \)
- Total Surface Area = \( 3872 \text{ cm}^2 \)