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.

Answer 1

First, let's find the area of the whole cookie cake.

The formula to calculate the area of a circle is A = πr^2, where r is the radius.

Given that the diameter of the cookie cake is 18 in, the radius would be half of that, which is 9 in.

So, the area of the whole cookie cake would be A = π(9)^2 = 81π ≈ 254.5 square inches.

Now, the missing section forms an angle of 270° out of a possible 360°, so the sector of the circle that is eaten would be 270°/360° = 3/4 of the whole circle.

To find the area of the eaten part, multiply the area of the whole cookie cake by 3/4:

Area eaten = (3/4) * 81π ≈ 190.9 square inches.

Therefore, the area of the cookie cake that was eaten is approximately 190.9 square inches.