Find the curved surface area and the total surface area of a right circular cyclinder whose height is 15 cm and the diameter of the cross- sections is 14 cm

Answer

To find the curved surface area and the total surface area of a right circular cylinder with a height of 15 cm and a diameter of 14 cm, follow these steps:

### Step 1: Identify the given values
- Height (H) of the cylinder = 15 cm
- Diameter of the cylinder = 14 cm

### Step 2: Calculate the radius (R)
The radius is half of the diameter.
\[ R = \frac{\text{Diameter}}{2} = \frac{14 \text{ cm}}{2} = 7 \text{ cm} \]

### Step 3: Calculate the curved surface area (CSA)
The formula for the curved surface area of a cylinder is:
\[ \text{Curved Surface Area} = 2 \pi R H \]
Substituting the values of \(R\) and \(H\):
\[ \text{CSA} = 2 \times \frac{22}{7} \times 7 \times 15 \]
Now simplify:
- The \(7\) in the numerator and denominator cancels out:
\[ \text{CSA} = 2 \times 22 \times 15 \]
Calculating:
\[ \text{CSA} = 44 \times 15 = 660 \text{ cm}^2 \]

### Step 4: Calculate the total surface area (TSA)
The formula for the total surface area of a cylinder is:
\[ \text{Total Surface Area} = 2 \pi R (R + H) \]
Substituting the values of \(R\) and \(H\):
\[ \text{TSA} = 2 \times \frac{22}{7} \times 7 \times (7 + 15) \]
Calculating \(7 + 15\):
\[ 7 + 15 = 22 \]
Now substituting back:
\[ \text{TSA} = 2 \times \frac{22}{7} \times 7 \times 22 \]
Again, the \(7\) cancels out:
\[ \text{TSA} = 2 \times 22 \times 22 \]
Calculating:
\[ \text{TSA} = 44 \times 22 = 968 \text{ cm}^2 \]

### Final Answers:
- Curved Surface Area = 660 cm²
- Total Surface Area = 968 cm²