Answer:
16.75
Step-by-step explanation:
To find the area of Francisco's larger slice of pie, we need to calculate the area of a sector of a circle. The given problem states that the pie has a diameter of 8 inches, and the larger slices each have a central angle of \( \theta = 120^\circ \).
First, we calculate the radius r of the pie:
r = diameter/2= 8/2 = 4 \text{ inches}
\]
The formula for the area of a sector of a circle is:
\[
\text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]
Substituting the given values:
\[
\text{Area of sector} = \frac{120^\circ}{360^\circ} \times \pi \times 4^2
\]
Simplify the fraction:
\[
\frac{120^\circ}{360^\circ} = \frac{1}{3}
\]
Now substitute this back into the formula:
\[
\text{Area of sector} = \frac{1}{3} \times \pi \times 16 = \frac{16\pi}{3}
\]
To find the numerical value, approximate \( \pi \) as 3.14:
\[
\text{Area of sector} = \frac{16 \times 3.14}{3} = \frac{50.24}{3} \approx 16.75 \text{ square inches}
\]
Thus, the area of Francisco’s larger slice of pie is closest to:
\[
\boxed{16.75}
\]