Answer:
Lee has more pizza
Lee has 2.24 in^2 more than John
Step-by-step explanation:
step 1
Find the area of each slice of pizza
[tex]A=\frac{1}{8}\pi r^{2}[/tex]
we have
[tex]r=16/2=8\ in[/tex] ----> the radius is half the diameter
substitute
[tex]A=\frac{1}{8}\pi 8^{2}[/tex]
[tex]A=8\pi\ in^{2}[/tex]
step 2
Find the area of John's part (area of shaded triangle)
The measure of the central angle of each slice of pizza is equal to
[tex]360\°/8=45\°[/tex]
so
the height of triangle is equal to the base
Let
x ---->the base of the shaded triangle
[tex]cos(45\°)=\frac{x}{r}[/tex]
[tex]cos(45\°)=\frac{x}{8}[/tex]
Remember that
[tex]cos(45\°)=\frac{\sqrt{2}}{2}[/tex]
substitute
[tex]\frac{\sqrt{2}}{2}=\frac{x}{8}[/tex]
solve for x
[tex]x=4\sqrt{2}\ in[/tex]
Find the area of shaded triangle
[tex]A=(1/2)(4\sqrt{2})(4\sqrt{2})=16\ in^2[/tex]
step 3
Find the area of Lee's part
The area of Lee's part is equal to the area of two slices of pizza minus the area of two triangles
so
[tex]2(8\pi)-2(16)=(16\pi-32)\ in^2[/tex]
assume
[tex]\pi =3.14[/tex]
[tex](16(3.14)-32)=18.24\ in^2[/tex]
so
Lee's part is greater than John part's
Find the difference
[tex]18.24-16=2.24\ in^2[/tex]
therefore
Lee has more pizza
Lee has 2.24 in^2 more than John
