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-by-Step Solution:

1. **Identify the dimensions of the cylinder and hemisphere:**
- Height of the cylinder (h) = 10 cm
- Radius of the cylinder (r) = 3.5 cm
- Since the hemispheres are scooped out from both ends, their radius will also be the same as that of the cylinder, which is 3.5 cm.

2. **Calculate the curved surface area (CSA) of the cylinder:**
The formula for the curved surface area of a cylinder is given by:
\[ \text{CSA of cylinder} = 2\pi rh \]
Substituting the values:
\[ \text{CSA of cylinder} = 2 \times \frac{22}{7} \times 3.5 \times 10 \]

3. **Calculate the CSA of one hemisphere:**
The formula for the curved surface area of a hemisphere is:
\[ \text{CSA of hemisphere} = 2\pi r^2 \]
Substituting the radius:
\[ \text{CSA of one hemisphere} = 2 \times \frac{22}{7} \times (3.5)^2 \]

4. **Calculate the total CSA of both hemispheres:**
Since there are two hemispheres:
\[ \text{Total CSA of hemispheres} = 2 \times \text{CSA of one hemisphere} \]

5. **Combine the areas to find the total surface area of the article:**
The total surface area (TSA) of the article is given by:
\[ \text{TSA} = \text{CSA of cylinder} + \text{Total CSA of hemispheres} \]

6. **Substituting the values and calculating:**
- Calculate CSA of the cylinder:
\[ \text{CSA of cylinder} = 2 \times \frac{22}{7} \times 3.5 \times 10 = 2 \times \frac{22}{7} \times 35 = \frac{1540}{7} = 220 \text{ cm}^2 \]
- Calculate CSA of one hemisphere:
\[ \text{CSA of one hemisphere} = 2 \times \frac{22}{7} \times (3.5)^2 = 2 \times \frac{22}{7} \times 12.25 = \frac{541}{7} = 77 \text{ cm}^2 \]
- Total CSA of both hemispheres:
\[ \text{Total CSA of hemispheres} = 2 \times 77 = 154 \text{ cm}^2 \]
- Total Surface Area:
\[ \text{TSA} = 220 + 154 = 374 \text{ cm}^2 \]

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