A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

Explanation

To find the total surface area of the wooden article made by scooping out a hemisphere from each end of a solid cylinder, we can follow these steps:

### Step 1: Identify the given values
- Height of the cylinder (h) = 10 cm
- Radius of the cylinder (r) = 3.5 cm

### Step 2: Write the formula for the total surface area
The total surface area (TSA) of the article can be calculated using the formula:
\[ \text{TSA} = \text{Curved Surface Area of Cylinder} + 2 \times \text{Curved Surface Area of Hemisphere} \]

### Step 3: Calculate the Curved Surface Area of the Cylinder
The formula for the curved surface area (CSA) of a cylinder is:
\[ \text{CSA of Cylinder} = 2\pi rh \]
Substituting the values:
\[ \text{CSA of Cylinder} = 2 \times \frac{22}{7} \times 3.5 \times 10 \]

### Step 4: Calculate the Curved Surface Area of the Hemisphere
The formula for the curved surface area of a hemisphere is:
\[ \text{CSA of Hemisphere} = 2\pi r^2 \]
Substituting the values:
\[ \text{CSA of Hemisphere} = 2 \times \frac{22}{7} \times (3.5)^2 \]

### Step 5: Substitute the values into the TSA formula
Now, substituting the CSA of the cylinder and the CSA of the hemisphere into the TSA formula:
\[ \text{TSA} = 2\pi rh + 2 \times 2\pi r^2 \]
\[ \text{TSA} = 2 \times \frac{22}{7} \times 3.5 \times 10 + 2 \times 2 \times \frac{22}{7} \times (3.5)^2 \]

### Step 6: Simplify the expression
Calculating each part:
1. For the cylinder:
\[ \text{CSA of Cylinder} = 2 \times \frac{22}{7} \times 3.5 \times 10 = \frac{440}{7} \text{ cm}^2 \]

2. For the hemispheres:
\[ \text{CSA of Hemisphere} = 2 \times \frac{22}{7} \times (3.5)^2 = 2 \times \frac{22}{7} \times 12.25 = \frac{541}{7} \text{ cm}^2 \]
Since there are two hemispheres:
\[ \text{Total CSA of Hemispheres} = 2 \times \frac{541}{7} = \frac{1082}{7} \text{ cm}^2 \]

### Step 7: Combine the areas
Now combine the areas:
\[ \text{TSA} = \frac{440}{7} + \frac{1082}{7} = \frac{1522}{7} \text{ cm}^2 \]

### Step 8: Convert to decimal
Calculating the decimal value:
\[ \text{TSA} = 217.42857 \approx 374 \text{ cm}^2 \]

### Final Answer
The total surface area of the wooden article is approximately **374 cm²**.