A cookie cake has a diameter of 18 in. If part of the cookie cake is eaten, the missing section forms an angle of 270°. What is the area of the cookie cake that was eaten? Round your answer to the nearest tenth.(1 point)

Responses

A = 63.6 in²
A = 63.6 in²

A = 127.2 in²
A = 127.2 in²

A = 190.9 in²

1 answer

To find the area of the cookie cake that was eaten, we start by calculating the total area of the cookie cake using the formula for the area of a circle:

\[ \text{Area} = \pi r^2 \]

The diameter of the cookie cake is given as 18 inches, so the radius \( r \) is:

\[ r = \frac{18}{2} = 9 \text{ inches} \]

Now we can calculate the total area:

\[ \text{Total Area} = \pi (9)^2 = \pi \times 81 = 81\pi \]

Using \( \pi \approx 3.14 \):

\[ \text{Total Area} \approx 81 \times 3.14 \approx 254.34 \text{ in}² \]

Now, we know that the angle of the missing section is 270°. Since a full circle is 360°, the fraction of the cookie cake that is eaten is:

\[ \text{Fraction Eaten} = \frac{270}{360} = \frac{3}{4} \]

To find the area of the eaten section, we multiply the total area by the fraction eaten:

\[ \text{Area Eaten} = \frac{3}{4} \times 254.34 \approx 190.9 \text{ in}² \]

Thus, the area of the cookie cake that was eaten is approximately:

\[ A \approx 190.9 \text{ in}² \]

So the correct answer is:

A = 190.9 in²