The radii of the circular faces of the frustum are 20 cm and 12 cm respectively . If the height of the frustum is 15 cm , then find its slant height.

Answer

To find the slant height of the frustum, we can follow these steps:

### Step 1: Identify the given values
- Radius of the top circular face (R1) = 20 cm
- Radius of the bottom circular face (R2) = 12 cm
- Height of the frustum (h) = 15 cm

### Step 2: Use the formula for slant height
The formula for the slant height (l) of a frustum is given by:
\[ l = \sqrt{h^2 + (R1 - R2)^2} \]

### Step 3: Calculate the difference in radii
Calculate \( R1 - R2 \):
\[ R1 - R2 = 20 \, \text{cm} - 12 \, \text{cm} = 8 \, \text{cm} \]

### Step 4: Substitute the values into the formula
Now substitute the values into the formula:
\[ l = \sqrt{15^2 + (8)^2} \]

### Step 5: Calculate the squares
Calculate \( 15^2 \) and \( 8^2 \):
\[ 15^2 = 225 \]
\[ 8^2 = 64 \]

### Step 6: Add the squares
Add the results:
\[ 225 + 64 = 289 \]

### Step 7: Take the square root
Now take the square root:
\[ l = \sqrt{289} = 17 \, \text{cm} \]

### Final Answer
The slant height of the frustum is **17 cm**.

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