Respuesta :
ANSWER:
2nd option: 82.43 ft²
STEP-BY-STEP EXPLANATION:
To calculate the area of the slice, we must first calculate the area of the circle completely, using the following formula:
[tex]\begin{gathered} A=\pi r^2 \\ \\ \text{ Note that the radius is half the diameter. } \\ \\ r=\frac{30}{2}=15\text{ ft} \\ \\ \text{ Therefore:} \\ \\ A=3.14\cdot15^2 \\ \\ A=706.5\text{ ft}^2 \end{gathered}[/tex]Now if we can calculate the value of the slice taking into account the following proportion:
[tex]\begin{gathered} A_s=706.5\cdot\frac{42\degree}{360\degree} \\ \\ A_s=82.43\text{ ft}^2 \end{gathered}[/tex]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
