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°)

The area of each slice of cake is

Step-by-step explanation:

step 1

Find the area of the complete cake

The area of the circle is equal to

we have

----> the radius is half the diameter

substitute

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

so

Using proportion

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

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

so then what are you asking?

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.