Alekos Pizza has delivered a beautiful 18 inch diameter pie

Aleko\'s Pizza has delivered a beautiful 18 inch diameter pie to Lee\'s dorm room. The pie is sliced into 8 equal sized pieces, but Lee is such a non-conformist he cuts off an edge as pictured. John then takes one of the remaining triangular slices.

Who has more pizza?

By how much? (Round your answer to two decimal places.)

Solution

Solution:
The Part in question of the Pie is call the Sector (1/4 of the Pie)
Area of the Pie or Circle divided by four equal parts

Area of the Circle = /4 x Diamenter²
Area of the Circle = /4 x 18²
Area of the Circle = 81
One Forth Area of the Circle is the Area Concern = 81 / 4
This area is also called SECTOR (AS) = 81 / 4

AS = 20.25 Take note


Lee’s in Geometry is call Segment
Area of segment = AS – Area of triangle ABC
Angle involve (AI)= ½ x 90°
Angle involve (AI) = 45°
Our Aim is to get distance BD
Triangle ABC = Triangle ACD
Line BC = Line CD

From Trigonometry :
Sin /2 = BC / (18/2)
Sin 90/2 = BC / (9)
BC = 9 Sin 45
BC = 9(0.707)
BC = 6.36
Share of John = ½ BC x AC
AC = [(AB)² - (BC)²
AC = [9² - 6.36²]
AC = [81 – 40.45]
AC = 6.37

Share of John = ½ BC x AC
Share of John = ½ (6.36) x (6.37)

Share of John = 20.26 Ans

Share of Lee = Is the segment of the SECTOR
Segment = Area of the SECTOR – Area of Triangle ABD
Area of Triangle ABD = 2 x Area of Triangle ABC
Or Area of Triangle ABD = 2 x Share of John

Area of Triangle ABD = 2 (20.26)

Area of Triangle ABD = 40.52

Lee’s Share = Area Of SECTOR – Area Triangle ABD
Lee’s Share = AS – ABD
Lee’s Share = 20.25 – 40.52  
Lee’s Share = 23.10 ,Ans
Lee’s Share is bigger than John’s