Question

PLEASE HELP!!!

Answer 1

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

$A=\frac{1}{8}\pi r^{2}$

we have

$r=16/2=8\ in$ ----> the radius is half the diameter

substitute

$A=\frac{1}{8}\pi 8^{2}$

$A=8\pi\ in^{2}$

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

$360\°/8=45\°$

so

the height of triangle is equal to the base

Let

x ---->the base of the shaded triangle

$cos(45\°)=\frac{x}{r}$

$cos(45\°)=\frac{x}{8}$

Remember that

$cos(45\°)=\frac{\sqrt{2}}{2}$

substitute

$\frac{\sqrt{2}}{2}=\frac{x}{8}$

solve for x

$x=4\sqrt{2}\ in$

Find the area of shaded triangle

$A=(1/2)(4\sqrt{2})(4\sqrt{2})=16\ in^2$

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

$2(8\pi)-2(16)=(16\pi-32)\ in^2$

assume

$\pi =3.14$

$(16(3.14)-32)=18.24\ in^2$

so

Lee's part is greater than John part's

Find the difference

$18.24-16=2.24\ in^2$

therefore

Lee has more pizza

Lee has 2.24 in^2 more than John