If the radus of two circular ends of a busket are `5//2` cm and 1 cm respectively and its height is 6 cm then find the slant height of frustum.

Answer

To find the slant height of the frustum of a cone (the basket in this case), we can use the formula:

\[ l = \sqrt{h^2 + (R - r)^2} \]

where:
- \( l \) is the slant height,
- \( h \) is the height of the frustum,
- \( R \) is the radius of the larger circular end,
- \( r \) is the radius of the smaller circular end.

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius of the larger circular end, \( R = \frac{5}{2} \) cm
- Radius of the smaller circular end, \( r = 1 \) cm
- Height of the frustum, \( h = 6 \) cm

2. **Convert the radius of the larger circular end to decimal**:
\[ R = \frac{5}{2} = 2.5 \text{ cm} \]

3. **Substitute the values into the formula**:
\[ l = \sqrt{h^2 + (R - r)^2} \]
\[ l = \sqrt{6^2 + (2.5 - 1)^2} \]

4. **Calculate \( R - r \)**:
\[ R - r = 2.5 - 1 = 1.5 \text{ cm} \]

5. **Square the height and the difference of the radii**:
\[ h^2 = 6^2 = 36 \]
\[ (R - r)^2 = (1.5)^2 = 2.25 \]

6. **Add the squares**:
\[ l = \sqrt{36 + 2.25} = \sqrt{38.25} \]

7. **Calculate the square root**:
\[ l \approx 6.18 \text{ cm} \quad (\text{using a calculator}) \]

### Final Answer:
The slant height \( l \) of the frustum is approximately \( 6.18 \) cm.

---