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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

Sagot :

step 1

Find out the area of the complete pie

[tex]A=pi*r^2[/tex]

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

substitute

[tex]\begin{gathered} A=pi*15^2 \\ A=225pi\text{ ft}^2 \end{gathered}[/tex]

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

[tex]\begin{gathered} \frac{225pi}{360^o}=\frac{x}{42^o} \\ \\ x=\frac{225p\imaginaryI}{360^{o}}*42^o \\ \\ x=26.25pi \\ x=26.25*3.14 \\ x=82.43\text{ ft}^2 \end{gathered}[/tex]

The answer is 82.43 ft2

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