The problem states that a spinner is a circle divided into 8 congruent pieces. The diameter of the circle is given as 16 cm. We need to find the area of each piece to the nearest tenth.

1. Problem Description

The problem states that a spinner is a circle divided into 8 congruent pieces. The diameter of the circle is given as 16 cm. We need to find the area of each piece to the nearest tenth.

2. Solution Steps

First, we need to find the radius of the circle. The radius is half of the diameter.

$radius = \frac{diameter}{2}$

$radius = \frac{16 cm}{2}$

$radius = 8 cm$

Next, we need to find the area of the entire circle. The formula for the area of a circle is:

$Area = \pi r^2$

$Area = \pi (8 cm)^2$

$Area = \pi (64 cm^2)$

$Area = 64\pi cm^2$

Since the circle is divided into 8 congruent pieces, we can find the area of one piece by dividing the total area by

8. $Area_{piece} = \frac{Area}{8}$

$Area_{piece} = \frac{64\pi cm^2}{8}$

$Area_{piece} = 8\pi cm^2$

Now, we need to approximate the value of $\pi$ as 3.14159 and calculate the area of one piece.

$Area_{piece} = 8 \times 3.14159 cm^2$

$Area_{piece} = 25.13272 cm^2$

Finally, we need to round the area to the nearest tenth.

$Area_{piece} \approx 25.1 cm^2$

3. Final Answer

The area of each piece is approximately $25.1 cm^2$.