Question

You’re baking a circular cake for a party. Your cake can be any size you want. What will the radius of your cake be and how many slices will you be able to cut? List the coordinates of any point in the coordinate plane. What is one topic that you learned about in this unit that could be used in real life?

Answer 1

1) R=20, feed about 35, 360/35=10 degrees/slice, Arc length 35/360*C= 35/360*125.66=12.2....12.21*2=24.43 inches, C=2(pie)r=20*2*(3.14)=125.66
2) If you would to open a bakery knowing how to find the area and circumference of your bake good is a good idea because you will be able to tell your consumers how many people the cake, pie, ect., should feed.

~GENERAL OUT~

Answer 2

What will the radius of your cake be?

This is a problem of geometry. Given that the cake is circular, the greater the cake the greater the radius of it. So, as shown in the figure 1, the radius will be the distance from the center to any extreme point of the circle.

How many slices will you be able to cut?

The total area of a circle is given by:


`A= \pi r^(2)`

We need to fin how many slices will be cut, so let's calculate the area of the circular sector which can be obtained simply applying rule of three, so:


`A_(cs)= \pi r^(2) ( (\theta)/(2 \pi ) )= (r^(2)\theta)/(2)`

Let's name n the number of slices, if we divide the total area by n this result, each area
`(\pi r^(2) )/(n)` must equal
`A_(cs)`, then:


`(\pi r^(2) )/(n)=(r^(2)\theta)/(2)`

Finally, we will be able to cut:


`n= (2 \pi )/(\theta)` Slices

List the coordinates of any point in the coordinate plane

Given that this is a circle, any point in the coordinate plane is given by this inequality:


`x^(2)+y^(2) \leq r^(2)`

What is one topic that you learned about in this unit that could be used in real life?

We can use geometry in real life, so in this problem we are able to cut and share a cake fairly.