Rajeet’s pumpkin pie is 10 inches in diameter. His family eats five out of the eight slices of pie, forming an angle of 225°. What area of the pie that was eaten?(1 point)

Question

Responses

A=15.625π in.2
upper A equals 15.625 pi in. squared

A=37.5π in.2
upper A equals 37.5 pi in. squared

A=25π in.2
upper A equals 25 pi in. squared

A=9.375π in.2
upper A equals 9.375 pi in. squared

Answer 1

To find the area of the pie that was eaten, we need to first determine the area of the whole pie and then calculate the area corresponding to the 225° angle that was consumed.

1. Calculate the area of the entire pie (which is a circle):

   The formula for the area \( A \) of a circle is: \[ A = \pi r^2 \] where \( r \) is the radius. Since the diameter of the pie is 10 inches, the radius \( r \) is: \[ r = \frac{10}{2} = 5 \text{ inches} \] Now we can calculate the area: \[ A = \pi (5^2) = \pi (25) = 25\pi \text{ in}^2 \]

2. Determine the fraction of the pie that was eaten:

   The pie was cut into 8 slices, and 5 slices were eaten. The angle taken by the eaten slices is 225°. Since the whole circle is 360°, the fraction of the pie that corresponds to the 225° angle can be determined as: \[ \text{Fraction of the pie eaten} = \frac{225}{360} = \frac{5}{8} \]

3. Calculate the area that was eaten:

   To find the area consumed, we multiply the total area of the pie by the fraction of the pie eaten: \[ A_{\text{eaten}} = A_{\text{total}} \times \text{Fraction eaten} \] \[ A_{\text{eaten}} = 25\pi \times \frac{5}{8} = \frac{125\pi}{8} \text{ in}^2 \]

   To further simplify: \[ \frac{125}{8} = 15.625 \]

   Hence, \[ A_{\text{eaten}} = 15.625\pi \text{ in}^2 \]

Thus, the area of pie that was eaten is:

A = 15.625π in².

So the correct response is:

A = 15.625π in².