Question

Sarah's mom bought her a cookie cake for her birthday. It had a diameter of 16 inches. Sarah's little brother ate part of the cookie cake. The missing section forms an angle of 270 degrees. What is the area of the cookie cake that was eaten? Round your answer to the nearest tenth. (1 point)
area =

in2

Answer 1

To find the area of the part of the cookie cake that was eaten, we can first calculate the total area of the cookie cake and then determine the area corresponding to the 270-degree angle that was eaten.

1. **Calculate the total area of the cookie cake**:
The area \(A\) of a circle is given by the formula:

\[
A = \pi r^2
\]

where \(r\) is the radius of the circle. The diameter of the cookie cake is 16 inches, hence the radius \(r\) is:

\[
r = \frac{16}{2} = 8 \text{ inches}
\]

Now, substituting the radius into the area formula:

\[
A = \pi (8^2) = \pi (64) = 64\pi
\]

Approximating \(\pi \approx 3.14\):

\[
A \approx 64 \times 3.14 = 200.96 \text{ in}^2
\]

2. **Calculate the area of the eaten section**:
The angle of the eaten section is 270 degrees. To find the area of that portion, we recognize that 270 degrees is \(\frac{270}{360} = \frac{3}{4}\) of the full circle.

Thus, the area of the eaten section \(A_{\text{eaten}}\) is:

\[
A_{\text{eaten}} = \frac{3}{4} A = \frac{3}{4} (64\pi) = 48\pi
\]

Again, approximating \(\pi\) as 3.14:

\[
A_{\text{eaten}} \approx 48 \times 3.14 = 150.72 \text{ in}^2
\]

3. **Round to the nearest tenth**:

\[
A_{\text{eaten}} \approx 150.7 \text{ in}^2
\]

So, the area of the cookie cake that was eaten is:

\[
\text{area} = 150.7 \text{ in}^2
\]