A cemi cylindrical piece of wood with height 40cm and diameter 28cm was painted all round , What is the area in square centimeters

To calculate the total area of the semi-cylindrical piece of wood that was painted, we need to determine the areas of all the surfaces that were painted.

Given:
- Height \( h = 40 \) cm
- Diameter \( d = 28 \) cm
- Radius \( r = \frac{d}{2} = 14 \) cm

### Step 1: Curved Surface Area (CSA)
The curved surface area of a full cylinder is given by:
\[
\text{CSA of full cylinder} = 2\pi rh
\]
Since it's a semi-cylinder, the curved surface area will be:
\[
\text{CSA of semi-cylinder} = \pi rh = \pi \times 14 \times 40 = 560\pi \ \text{cm}^2
\]

### Step 2: Area of the two semi-circular ends
Each end is a semi-circle, so the area of one semi-circular end is:
\[
\text{Area of one semi-circular end} = \frac{1}{2} \times \pi r^2 = \frac{1}{2} \times \pi \times 14^2 = 98\pi \ \text{cm}^2
\]
Since there are two ends:
\[
\text{Area of both semi-circular ends} = 2 \times 98\pi = 196\pi \ \text{cm}^2
\]

### Step 3: Area of the rectangular base
The rectangular base has dimensions \(2r\) by \(h\):
\[
\text{Area of rectangular base} = 2r \times h = 2 \times 14 \times 40 = 1120 \ \text{cm}^2
\]

### Step 4: Total Surface Area
Adding up all the painted areas:
\[
\text{Total Surface Area} = \text{CSA of semi-cylinder} + \text{Area of both semi-circular ends} + \text{Area of rectangular base}
\]
\[
\text{Total Surface Area} = 560\pi + 196\pi + 1120 = 756\pi + 1120 \ \text{cm}^2
\]
\[
\text{Total Surface Area} \approx 756 \times 3.14 + 1120 = 2371.44 + 1120 = 3491.44 \ \text{cm}^2
\]

Thus, the area in square centimeters is approximately **3491.44 cm²**.

Would you like more details or have any questions?

Here are five related questions:
1. How do you calculate the surface area of a full cylinder?
2. What is the difference in the area between a semi-cylinder and a full cylinder?
3. How would the area change if the cylinder were hollow?
4. What are the applications of calculating surface area in real life?
5. How does the radius affect the curved surface area of a cylinder?

**Tip:** Always double-check the dimensions used in calculations to avoid errors, especially when converting between radius and diameter.

A semi-cylindrical piece of wood with height 40cm and diameter 28cm was painted all round. What is the area in square centimeters?

Calculate the surface area of a semi-cylindrical piece of wood with a height of 40cm and a diameter of 28cm. This problem involves geometry concepts like curved surface area and areas of semi-circles and rectangles. Perfect for Grades 9-12 students.

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