Question

You have a cake that is 10 inches in diameter. You expect 12 people to share it, so you cut it into 12
equal slices. What is the area of each slice of cake? (Hint: the entire cake is 360°)

Answer 1

Answer:

The area of each slice of cake is $\frac{25}{12}\pi\ in^2$

Step-by-step explanation:

step 1

Find the area of the complete cake

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=10/2=5\ in$ ----> the radius is half the diameter

substitute

$A=\pi (5)^{2}$

$A=25\pi\ in^2$

step 2

Find the area of each slice of cake

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

If you cut the cake into 12 equal slices

then

the central angle of each slice is equal to $\frac{360^o}{12}=30^o$

so

Using proportion

Find out the area of each slice for a central angle of 30 degrees

$\frac{25\pi}{360^o}=\frac{x}{30^o} \\\\x= \frac{25\pi}{360^o}(30^o)\\\\x=\frac{25}{12}\pi\ in^2$

Note This problem could be solved by directly dividing the area of the circle by 12, however, proportions and concepts of central angle were applied for didactic purposes