Question

A giant pie is created in an attempt to break a world record for baking. The pie is shown below:What is the area of the slice of pie that was cut, rounded to the nearest hundredth? 78.13 ft2 82.43 ft2 86.31 ft2 91.98 ft2

Answer 1

step 1

Find out the area of the complete pie

`A=pi*r^2`

r=30/2=15 ft ----> the radius is half the diameter

substitute

`\begin{gathered} A=pi*15^2 \\ A=225pi\text{ ft}^2 \end{gathered}`

Remember that the area of a complete circle, subtends a central angle of 360 degrees

so

Applying proportion

Find out the area for a central angle of 42 degrees

`\begin{gathered} (225pi)/(360^o)=(x)/(42^o) \\ \\ x=(225p\imaginaryI)/(360^(o))*42^o \\ \\ x=26.25pi \\ x=26.25*3.14 \\ x=82.43\text{ ft}^2 \end{gathered}`

The answer is 82.43 ft2