*Today is Pi Day! Below are a few questions to celebrate.*

If June ate 1/4 of 2/3 of 1/2 of a pie, what fraction of the whole pie did she eat? Express your answer as a common fraction.

*To determine what fraction of the pie June ate, we can multiply (1/4)(2/3)(1/2) = 2/24 = 1/12. So, June ate ***1/12 ***of the pie.*

If the top surface of a particular slice of pie is a sector of a circle with a vertex angle measuring 20 degrees and the length of the arc is π units, what is the circumference of the top surface of the whole pie? Express your answer in terms of π.

*Since the sector has a vertex angle that measures 20 degrees, the sector is 20/360 = 1/18 of the whole pie. Thus, the arc (which is π units) is 1/18 of the whole pie’s circumference. So, the whole circumference of the pie must be ***18π ***units.*

What is the perimeter of the top surface of the remaining portion of the pie if only the slice described in question 2 is removed? Express your answer in terms of π.

*When the sector described above is removed, the remaining circumference is 18π – π = 17π. To this, we must add the length of 2 radii for where the cuts were made to remove the piece of pie. Since the whole pie’s circumference is 18π, the radius can be found using the equation C = 2πr: 18π = 2πr → r = 9. Thus, the total perimeter is 2(9) + 17π = ***18 + 17π*** units.*

**♦ Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.**

**Page 2 contains ONLY PROBLEMS. ♦**