Diameter of a right circular cylinder is 10 cm and hight is 14 cm,find its lateral surface.

Answer

To find the lateral surface area of a right circular cylinder, we can use the formula:

\[ \text{Lateral Surface Area} = 2 \pi r h \]

where \( r \) is the radius of the cylinder and \( h \) is the height.

### Step 1: Find the radius of the cylinder
Given the diameter of the cylinder is 10 cm, we can find the radius by using the formula:

\[ r = \frac{\text{Diameter}}{2} \]

Substituting the given diameter:

\[ r = \frac{10 \text{ cm}}{2} = 5 \text{ cm} \]

### Step 2: Identify the height of the cylinder
The height \( h \) of the cylinder is given as 14 cm.

### Step 3: Substitute the values into the lateral surface area formula
Now that we have the radius and height, we can substitute these values into the lateral surface area formula:

\[ \text{Lateral Surface Area} = 2 \pi r h = 2 \pi (5 \text{ cm})(14 \text{ cm}) \]

### Step 4: Calculate the lateral surface area
Now, we can perform the calculation:

\[ \text{Lateral Surface Area} = 2 \pi (5)(14) = 2 \pi (70) = 140 \pi \text{ cm}^2 \]

### Step 5: Approximate the value
Using \( \pi \approx 3.14 \):

\[ \text{Lateral Surface Area} \approx 140 \times 3.14 \approx 439.6 \text{ cm}^2 \]

### Final Answer
The lateral surface area of the cylinder is approximately \( 439.6 \text{ cm}^2 \).

---