Question

aghana cuts a pie with a 10 - inch diameter into 8 equal slices and eats one slice. how many square inches of pie are left? use 3.14 for π. round the final answer to the nearest tenth of a square inch. select all the true statements. the area of the whole pie is 314 in.²? the area of the whole pie is 78.5 in.²? the problem is asking for the area of a fractional piece of the pie. the solution is 9.2 in.²? the solution is 68.7 in.²?

Explanation:

Step1: Find the radius of the pie

The diameter of the pie is 10 inches, so the radius \( r=\frac{10}{2} = 5 \) inches.

Step2: Calculate the area of the whole pie

Using the formula for the area of a circle \( A=\pi r^{2} \), with \( \pi = 3.14 \) and \( r = 5 \), we get \( A=3.14\times5^{2}=3.14\times25 = 78.5 \) square inches. So the statement "The area of the whole pie is 78.5 in.²" is true, and "The area of the whole pie is 314 in.²" is false.

Step3: Analyze what the problem is asking

The problem is about finding the area of pie left after eating one slice. First, we need to find the area of one slice (fractional part) and then subtract from the whole. So "The problem is asking for the area of a fractional piece of the pie" (to find the area of one slice, which is a fractional part \( \frac{1}{8} \) of the whole) is true.

Step4: Calculate the area of one slice

The area of one slice is \( \frac{1}{8}\times78.5=\frac{78.5}{8}=9.8125 \) square inches.

Step5: Calculate the area left

Subtract the area of one slice from the whole: \( 78.5 - 9.8125=68.6875\approx68.7 \) square inches. So "The solution is 68.7 in.²" is true, and "The solution is 9.2 in.²" is false.

Answer:

• The area of the whole pie is 78.5 in.² (True)
• The problem is asking for the area of a fractional piece of the pie (True)
• The solution is 68.7 in.² (True)

(The false statements are "The area of the whole pie is 314 in.²" and "The solution is 9.2 in.²")