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°

Question

. What is the area of the cookie cake that was eaten? Round your answer to the nearest tenth.(1 point)
Responses

A=254.5 in.2
upper A equals 254.5 in. squared

A=127.2 in.2
upper A equals 127.2 in. squared

A=190.9 in.2
upper A equals 190.9 in. squared

A=63.6 in.2
upper A equals 63.6 in. squared

Answer 1

To find the area of the cookie cake that was eaten, we start by calculating the area of the entire cookie cake and then find the portion that corresponds to the missing section, which forms an angle of 270°.

1. Calculate the radius of the cookie cake:
   The diameter is 18 inches, so the radius \( r \) is:
   \[ r = \frac{diameter}{2} = \frac{18}{2} = 9 \text{ inches} \]

2. Calculate the area of the entire cookie cake:
   The area \( A \) of a circle is given by the formula:
   \[ A = \pi r^2 \]
   Substituting the radius:
   \[ A = \pi (9^2) = \pi(81) \approx 254.47 \text{ in}^2 \]

3. Calculate the fraction of the cake that was eaten based on the angle:
   The total angle in a circle is 360°. The eaten section forms an angle of 270°, so the fraction of the circle that was eaten is:
   \[ \text{Fraction eaten} = \frac{270}{360} = \frac{3}{4} \]

4. Calculate the area of the eaten section:
   The area of the eaten section is:
   \[ \text{Area eaten} = \frac{3}{4} \times 254.47 \text{ in}^2 \]
   \[ \text{Area eaten} \approx 190.9 \text{ in}^2 \]

Rounding to the nearest tenth, the area of the cookie cake that was eaten is approximately:

\[ \boxed{190.9} \text{ in}^2 \]