Question

A giant pie is created in an attempt to break a world record for baking. The pie is shown below:A circle is shown with a central angle marked 42 degrees and the diameter marked 30 feet.What is the area of the slice of pie that was cut, rounded to the nearest hundredth? 78.13 ft2 82.43 ft2 86.31 ft2 91.98 ft2

Answer 1

2nd option: 82.43 ft²

Explanation:

To calculate the area of the slice, we must first calculate the area of the circle completely, using the following formula:

`\begin{gathered} A=\pi r^2 \\ \\ \text{ Note that the radius is half the diameter. } \\ \\ r=(30)/(2)=15\text{ ft} \\ \\ \text{ Therefore:} \\ \\ A=3.14\cdot15^2 \\ \\ A=706.5\text{ ft}^2 \end{gathered}`

Now if we can calculate the value of the slice taking into account the following proportion:

`\begin{gathered} A_s=706.5\cdot(42\degree)/(360\degree) \\ \\ A_s=82.43\text{ ft}^2 \end{gathered}`

Therefore, the area of the slice is equal to 82.43 ft², that is to say that the correct answer is 2nd option: 82.43 ft²