Francisco used a -inch diameter pie dish to bake his favorite cherry pie. He cut it into unequal slices, as shown in the figure. He wanted a larger slice for himself. The two slices that are cut larger than the other four slices each have a central angle that measures . Which of the following is closest to the area, in square inches, of Franciso’s larger slice of pie



Answer :

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}

\]