The area of a circle of radius 8 cm is equal to the area of a triangle of base equal to 8 cm. Find the corresponding height of the triangle.

Options

A. `16picm`
B. `38 pi cm`
C. `18 pi cm`
D. `8 pi cm`

Answer

To solve the problem, we need to find the height of a triangle given that the area of the triangle is equal to the area of a circle with a radius of 8 cm.

### Step-by-Step Solution:

1. **Calculate the Area of the Circle:**
The formula for the area of a circle is given by:
\[ \text{Area of Circle} = \pi r^2 \]
Here, the radius \( r = 8 \) cm. Plugging in the value:
\[ \text{Area of Circle} = \pi (8)^2 = \pi \times 64 = 64\pi \text{ cm}^2 \]

2. **Set Up the Area of the Triangle:**
The formula for the area of a triangle is:
\[ \text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
The base of the triangle is given as 8 cm. Let the height be \( h \). Therefore, we can express the area of the triangle as:
\[ \text{Area of Triangle} = \frac{1}{2} \times 8 \times h = 4h \text{ cm}^2 \]

3. **Set the Areas Equal:**
According to the problem, the area of the triangle is equal to the area of the circle:
\[ 4h = 64\pi \]

4. **Solve for Height \( h \):**
To find \( h \), we divide both sides of the equation by 4:
\[ h = \frac{64\pi}{4} = 16\pi \text{ cm} \]

### Final Answer:
The corresponding height of the triangle is \( 16\pi \) cm.

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