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

Options

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

Explanation

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

### Step 1: Identify the given values
- Top radius (R) = 28 cm
- Bottom radius (r) = 7 cm
- Slant height (L) = 45 cm

### Step 2: Write 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:
- \( \pi \) is approximately \( \frac{22}{7} \) or \( 3.14 \)
- \( L \) is the slant height
- \( R \) is the radius of the top
- \( r \) is the radius of the bottom

### Step 3: Substitute the values into the formula
Now we substitute the values into the formula:
\[ \text{CSA} = \frac{22}{7} \times 45 \times (28 + 7) \]

### Step 4: Calculate the sum of the radii
Calculate \( R + r \):
\[ R + r = 28 + 7 = 35 \]

### Step 5: Substitute back into the formula
Now substitute back into the formula:
\[ \text{CSA} = \frac{22}{7} \times 45 \times 35 \]

### Step 6: Simplify the expression
First, calculate \( 45 \times 35 \):
\[ 45 \times 35 = 1575 \]
Now substitute this back:
\[ \text{CSA} = \frac{22}{7} \times 1575 \]

### Step 7: Calculate \( \frac{22}{7} \times 1575 \)
To simplify:
\[ \text{CSA} = 22 \times \frac{1575}{7} \]
Calculating \( \frac{1575}{7} \):
\[ \frac{1575}{7} = 225 \]
Now substitute this value back:
\[ \text{CSA} = 22 \times 225 \]

### Step 8: Final calculation
Now calculate \( 22 \times 225 \):
\[ 22 \times 225 = 4950 \]

### Conclusion
Thus, the curved surface area of the bucket is:
\[ \text{CSA} = 4950 \, \text{cm}^2 \]