The frustum of a right circular cone has the diameters of base 10 cm, of top 6 cm and a height of 5 cm. Find its slant height

Options

A. `29 cm `
B. `3vv3 cm `
C. `3 cm `
D. `4 vv 3 cm`

Answer

To find the slant height of the frustum of a right circular cone, we can follow these steps:

### Step 1: Identify the given values
- Diameter of the base (D) = 10 cm
- Diameter of the top (d) = 6 cm
- Height (h) = 5 cm

### Step 2: Calculate the radii
- Radius of the base (R) = D/2 = 10 cm / 2 = 5 cm
- Radius of the top (r) = d/2 = 6 cm / 2 = 3 cm

### Step 3: Use the formula for slant height
The formula for the slant height (L) of a frustum of a cone is given by:
\[ L = \sqrt{h^2 + (R - r)^2} \]

### Step 4: Substitute the values into the formula
- Substitute the values of height (h), radius of the base (R), and radius of the top (r):
\[ L = \sqrt{5^2 + (5 - 3)^2} \]

### Step 5: Calculate the squares
- Calculate \( 5^2 = 25 \)
- Calculate \( (5 - 3)^2 = 2^2 = 4 \)

### Step 6: Add the squares
- Add the results: \( 25 + 4 = 29 \)

### Step 7: Take the square root
- Finally, take the square root:
\[ L = \sqrt{29} \]

### Conclusion
The slant height of the frustum is \( \sqrt{29} \) cm.

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