Question

A large pizza has a diameter of 14 inches and can be cut into equal slices.

Answer 1

Part 1

Find out the circumference of the circle (pizza)

The formula is given by

`C=2*pi*r`

where

D=14 in

r=D/2=14/2=7 in ----> the radius is half the diameter

substitute

`\begin{gathered} C=2*pi*7 \\ C=14pi\text{ in} \end{gathered}`

The length is 14pi inches

Part 2

we have a central angle of 55 degrees

Find out the arc length

`\begin{gathered} arc\text{ length=}(55^o)/(360^o)*2*pi*7 \\ \\ arc\text{ length=}(770)/(360)pi\text{ in} \\ \\ arc\text{length=}\frac{\text{77}}{\text{36}}\text{pi in} \end{gathered}`

Part 3

Find out the arc length by a central angle of 40 degrees

Apply the formula

`\begin{gathered} arc\text{ length=}\frac{40^o}{\text{360}^o\text{{}}}*\text{2*p}\imaginaryI *\text{7} \\ \\ arc\text{ length=}(560)/(360)pi\text{ in} \\ \\ arc\text{ length=}(14)/(9)pi\text{ in} \end{gathered}`