Question

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) Responses A=25π in.2 upper A equals 25 pi in. squared A=9.375π in.2 upper A equals 9.375 pi in. squared A=15.625π in.2 upper A equals 15.625 pi in. squared A=37.5π in.2

Answer 1

To find the area of the pie that was eaten, we first need to calculate the total area of the whole pumpkin pie and then find the proportion of that area that corresponds to the angle of the slices eaten.

1. Calculate the radius of the pumpkin pie:

   • Diameter = 10 inches
   • Radius \( r = \frac{10}{2} = 5 \) inches

2. Calculate the total area of the pie: \[ \text{Area} = \pi r^2 = \pi (5^2) = 25\pi \text{ in}^2 \]

3. Find the proportion of the pie that was eaten:

   • The angle for the slices eaten is 225°.
   • The total angle of a circle is 360°.
   • The fraction of the pie eaten is: \[ \text{Fraction eaten} = \frac{225}{360} = \frac{5}{8} \]

4. Calculate the area of the pie that was eaten: \[ \text{Area eaten} = \text{Total area} \times \text{Fraction eaten} = 25\pi \times \frac{5}{8} \] \[ = \frac{125\pi}{8} \text{ in}^2 \] \[ = 15.625\pi \text{ in}^2 \]

So, the area of the pie that was eaten is \( 15.625\pi \) in².

Answer: A = 15.625π in²