area of circle

Question

A circular was made for John's birthday. John cut it into 22 equal pieces. If the top surface of each cake was 28cm². Find the circumference of the cake.

Answer 1

If the area of the top of each slice of cake is 28cm², then the total area if the top of the cake would be A=(22)(28)=616cm².

 

Using the two equations for area (A=πr²) and circumference (C=2πr) and eliminating radius (r), we have

A               =π(C/(2π))²

616           =C²/4π

(616)(4π) =C²

C               =√(2464π)cm

C               =4√(154π)cm

C               ≈87.98cm

Answer 2

Dear Sam,

     There is another way of doing this problem:

1.  Draw the cake and shade in one little piece,  Area of small piece=28 cm²  .

 

Question:  What is the circumference of the circular cake?

 

2.  Draw a picture to make the problem easier.

 

The small area piece=28 sq. cm.  We want to find the Area of the total surface of the cake, so we can find the radius of the total cake.

 

3.  Multiply  22* 28=616 sq. cm =  total area

 

4.  Use the Area of a circle equation:  A=pi* r²  .      616= π r²  .      Substitution

 

5.  Solve for "r"  by dividing both sides of equation by pi, and then take the square root of both sides:

 

√(616/pi)= √(r²)=r

 

6.  Now you can use the circumference formula:  C= 2pir=   2π( √(616/pi))= 87.982295 cm≅ 87.98

 

If I have helped you, please give me a thumbs up.

                                                                    Susan C.