Find the volume, curved surface area and total surface area of each of the cylinders whose dimensions are:
(i) radius of the base =7cm and height =50 cm
(ii) radius of the base =5.6 m and height =1.25 m
(iii) radius of the base k=14 dm and height =15 m

Answer

To solve the question of finding the volume, curved surface area (CSA), and total surface area (TAS) of the given cylinders, we will follow these steps for each part:

### Given Formulas:
1. **Volume (V)** of a cylinder:
\[ V = \pi r^2 h \]
2. **Curved Surface Area (CSA)** of a cylinder:
\[ CSA = 2 \pi r h \]
3. **Total Surface Area (TAS)** of a cylinder:
\[ TAS = 2 \pi r h + 2 \pi r^2 = 2 \pi r (h + r) \]

### Part (i): Radius = 7 cm, Height = 50 cm

1. **Calculate Volume**:
\[ V = \pi r^2 h = \frac{22}{7} \times (7)^2 \times 50 \]
\[ V = \frac{22}{7} \times 49 \times 50 = \frac{22 \times 2450}{7} = 7700 \text{ cm}^3 \]

2. **Calculate Curved Surface Area (CSA)**:
\[ CSA = 2 \pi r h = 2 \times \frac{22}{7} \times 7 \times 50 \]
\[ CSA = 2 \times 22 \times 50 = 2200 \text{ cm}^2 \]

3. **Calculate Total Surface Area (TAS)**:
\[ TAS = 2 \pi r (h + r) = 2 \times \frac{22}{7} \times 7 \times (50 + 7) \]
\[ TAS = 2 \times 22 \times 57 = 2508 \text{ cm}^2 \]

### Part (ii): Radius = 5.6 m, Height = 1.25 m

1. **Calculate Volume**:
\[ V = \pi r^2 h = \frac{22}{7} \times (5.6)^2 \times 1.25 \]
\[ V = \frac{22}{7} \times 31.36 \times 1.25 = \frac{22 \times 39.2}{7} = 123.2 \text{ m}^3 \]

2. **Calculate Curved Surface Area (CSA)**:
\[ CSA = 2 \pi r h = 2 \times \frac{22}{7} \times 5.6 \times 1.25 \]
\[ CSA = 2 \times 22 \times 1.25 \times 5.6 = 44 \times 5.6 = 246.4 \text{ m}^2 \]

3. **Calculate Total Surface Area (TAS)**:
\[ TAS = 2 \pi r (h + r) = 2 \times \frac{22}{7} \times 5.6 \times (1.25 + 5.6) \]
\[ TAS = 2 \times 22 \times 5.6 \times 6.85 = 241.12 \text{ m}^2 \]

### Part (iii): Radius = 14 dm, Height = 15 m (Convert radius to meters)

1. **Convert Radius**:
\[ \text{Radius} = 14 \text{ dm} = 1.4 \text{ m} \]

2. **Calculate Volume**:
\[ V = \pi r^2 h = \frac{22}{7} \times (1.4)^2 \times 15 \]
\[ V = \frac{22}{7} \times 1.96 \times 15 = \frac{22 \times 29.4}{7} = 92.4 \text{ m}^3 \]

3. **Calculate Curved Surface Area (CSA)**:
\[ CSA = 2 \pi r h = 2 \times \frac{22}{7} \times 1.4 \times 15 \]
\[ CSA = 2 \times 22 \times 1.4 \times 15 = 132 \text{ m}^2 \]

4. **Calculate Total Surface Area (TAS)**:
\[ TAS = 2 \pi r (h + r) = 2 \times \frac{22}{7} \times 1.4 \times (15 + 1.4) \]
\[ TAS = 2 \times 22 \times 1.4 \times 16.4 = 144.32 \text{ m}^2 \]

### Summary of Results:
- **Part (i)**: Volume = 7700 cm³, CSA = 2200 cm², TAS = 2508 cm²
- **Part (ii)**: Volume = 123.2 m³, CSA = 44 m², TAS = 241.12 m²
- **Part (iii)**: Volume = 92.4 m³, CSA = 132 m², TAS = 144.32 m²