We are given a rectangle with a semi-circle cut out. We need to find the area of the remaining region. The rectangle has length 22 cm and height 8 cm. The semi-circle's diameter spans the entire width of the rectangle except for two segments, each 4 cm in length, so the diameter of the semi-circle is $22 - 4 - 4 = 14$ cm. Thus, the radius is $14/2 = 7$ cm.

1. Problem Description

We are given a rectangle with a semi-circle cut out. We need to find the area of the remaining region. The rectangle has length 22 cm and height 8 cm. The semi-circle's diameter spans the entire width of the rectangle except for two segments, each 4 cm in length, so the diameter of the semi-circle is $22 - 4 - 4 = 14$ cm. Thus, the radius is $14/2 = 7$ cm.

2. Solution Steps

First, calculate the area of the rectangle.

Area of rectangle = length * height

$A_{rectangle} = 22 \times 8 = 176$ cm$^2$

Next, calculate the area of the semi-circle.

The area of a circle is given by $A = \pi r^2$. The area of a semi-circle is half of the area of a circle.

$A_{semi-circle} = \frac{1}{2} \pi r^2$

$A_{semi-circle} = \frac{1}{2} \pi (7^2) = \frac{1}{2} \pi (49) = \frac{49\pi}{2}$

We can approximate $\pi$ as $\frac{22}{7}$ to get a numerical value.

$A_{semi-circle} = \frac{49}{2} \times \frac{22}{7} = \frac{7}{1} \times \frac{11}{1} = 77$ cm$^2$

Now, subtract the area of the semi-circle from the area of the rectangle to find the area of the remaining part.

Area of remaining part = Area of rectangle - Area of semi-circle

$A_{remaining} = 176 - 77 = 99$ cm$^2$

3. Final Answer

The area of the remaining part is 99 cm$^2$.

Final Answer: B. 99 cm$^2$