Question

if a diameter of a small pizza is 8 in it's a small pizza is cut into 8 pieces what is the area of each piece in inches squared

Answer 1

we need a drawing

then the radius is hal diamter, so 4in

the total area of the pizza is

`A=\pi* r^2`
`\begin{gathered} A=\pi*4^2 \\ A=\pi*16 \\ A=16\pi \end{gathered}`

pizza is a circle, a whole circle has 360° if we cut the circle on 8 pieces the area of each pieces is represented by the angle

`(360)/(8)=45`

now if 16pi is the area to 360, whats the area to 45°(each piece)

`\begin{gathered} 360\longrightarrow16\pi \\ 45\longrightarrow x \end{gathered}`

where x is the area of each piece

To find the value of x we use corss multiplication

multiply 45 by 16pi and divide between 360

`\begin{gathered} x=(45*16\pi)/(360) \\ \\ x=2\pi\approx6.28 \end{gathered}`

the area of each piece of pizza is 2pi or 6.28 square inches