The slant height of a bucket is 45 cm and the radii of its top and and bottom are 28 cm and 7 cm respectively . The curved surface area of the bucket is

Options

A. `4953 cm^(2)`
B. `4952 cm^(2)`
C. `4951 cm^(2)`
D. `4950 cm^(2)`

Explanation

To find the curved surface area of a bucket in the shape of a frustum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius of the top (R) = 28 cm
- Radius of the bottom (r) = 7 cm
- Slant height (L) = 45 cm

2. **Use the formula for the curved surface area of a frustum:**
The formula for the curved surface area (CSA) of a frustum of a cone is given by:
\[ \text{CSA} = \pi L (R + r) \]
where \(L\) is the slant height, \(R\) is the radius of the top, and \(r\) is the radius of the bottom.

3. **Substitute the values into the formula:**
\[ \text{CSA} = \pi \times 45 \times (28 + 7) \]
\[ = \pi \times 45 \times 35 \]

4. **Calculate \(28 + 7\):**
\[ 28 + 7 = 35 \]

5. **Calculate the product:**
\[ \text{CSA} = \pi \times 45 \times 35 \]

6. **Use \(\pi \approx \frac{22}{7}\) for calculation:**
\[ \text{CSA} = \frac{22}{7} \times 45 \times 35 \]

7. **Calculate \(45 \times 35\):**
\[ 45 \times 35 = 1575 \]

8. **Now substitute back into the equation:**
\[ \text{CSA} = \frac{22}{7} \times 1575 \]

9. **Perform the multiplication:**
\[ = \frac{22 \times 1575}{7} \]

10. **Calculate \(22 \times 1575\):**
\[ 22 \times 1575 = 34650 \]

11. **Now divide by 7:**
\[ \text{CSA} = \frac{34650}{7} = 4950 \text{ cm}^2 \]

### Final Answer:
The curved surface area of the bucket is **4950 cm²**.