If h is the height, I the slant height and `r_(1), r_(2)` radii of the circular bases of the frustum of a cone, then slant height of the frustum = `sqrt(( r_(1) - r_(2))^(2) + h^(2))`. Find the height of the cone of which the frustum is a part = (h`r_(1)`/(`r_(1) - r_(2)`).We have a bucket in the form of frustum of a cone in which h = 8 cm, `r_(1)` = 9 cm and `r_(2)` = 3 cm.

Options

A. 12 cm
B. 9 cm
C. 11 cm
D. 8 cm

Answer

To find the height of the cone of which the frustum is a part, we will use the formula provided in the question. Let's break down the steps:

### Step 1: Identify the given values
- Height of the frustum (h) = 8 cm
- Radius of the upper base (r1) = 9 cm
- Radius of the lower base (r2) = 3 cm

### Step 2: Write down the formula for the height of the cone
The formula to find the height (H) of the cone of which the frustum is a part is given by:
\[ H = \frac{h \cdot r_1}{r_1 - r_2} \]

### Step 3: Substitute the values into the formula
Now, substitute the values of h, r1, and r2 into the formula:
\[ H = \frac{8 \cdot 9}{9 - 3} \]

### Step 4: Calculate the denominator
Calculate \( r_1 - r_2 \):
\[ 9 - 3 = 6 \]

### Step 5: Substitute the denominator back into the equation
Now substitute this back into the equation:
\[ H = \frac{8 \cdot 9}{6} \]

### Step 6: Calculate the numerator
Calculate \( 8 \cdot 9 \):
\[ 8 \cdot 9 = 72 \]

### Step 7: Divide the numerator by the denominator
Now divide 72 by 6:
\[ H = \frac{72}{6} = 12 \]

### Step 8: State the final answer
Thus, the height of the cone of which the frustum is a part is:
\[ H = 12 \text{ cm} \]

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