The radii of the ends of a frustum of a cone 40 cm high are 38 cm and 8 cm. The slant height of the frustum of cone is

Options

A. 50 cm
B. `10sqrt7 cm `
C. `60.96 cm `
D. `4 sqrt2`

Answer

To find the slant height of a frustum of a cone, we can use the formula:

\[ L = \sqrt{h^2 + (R_1 - R_2)^2} \]

where:
- \( L \) is the slant height,
- \( h \) is the height of the frustum,
- \( R_1 \) is the radius of the larger base,
- \( R_2 \) is the radius of the smaller base.

### Step-by-Step Solution

1. **Identify the given values:**
- Height \( h = 40 \) cm
- Radius of the larger base \( R_1 = 38 \) cm
- Radius of the smaller base \( R_2 = 8 \) cm

2. **Calculate the difference of the radii:**
\[ R_1 - R_2 = 38 - 8 = 30 \text{ cm} \]

3. **Square the height and the difference of the radii:**
- Square of the height:
\[ h^2 = 40^2 = 1600 \text{ cm}^2 \]
- Square of the difference of the radii:
\[ (R_1 - R_2)^2 = 30^2 = 900 \text{ cm}^2 \]

4. **Add the squares:**
\[ h^2 + (R_1 - R_2)^2 = 1600 + 900 = 2500 \text{ cm}^2 \]

5. **Take the square root to find the slant height:**
\[ L = \sqrt{2500} = 50 \text{ cm} \]

### Final Answer
The slant height of the frustum of the cone is \( 50 \) cm.

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