a 40cm diameter birthday cake can feed 4 people.How many people will a 80 cm diameter cake feed?
16 people
I forgot the explanation. 40cm is the diameter but th radius is 20. This means the area of the 40cm cake is actually 400pi. The 80cm cake will then be 1600pi. You get it from there.
To find out how many people a larger diameter cake can feed, we can use the concept of area. The area of a circle is calculated using the formula A = πr^2, where A represents the area and r represents the radius (half the diameter) of the circle.
Given that the 40 cm diameter cake can feed 4 people, we need to calculate the radius of the cake. The radius (r) would be half of the diameter, so r = 40 cm / 2 = 20 cm.
Now, let's calculate the area of the 40 cm diameter cake using the formula:
A = πr^2
A = π(20 cm)^2
A = 400π cm^2
Since the area of the 40 cm diameter cake is 400π cm^2 and it can feed 4 people, each person would have approximately 100π cm^2 of cake.
To determine how many people an 80 cm diameter cake will feed, we can use the same approach. First, calculate the radius of the larger cake: r = 80 cm / 2 = 40 cm.
Now, calculate the area of the 80 cm diameter cake:
A = πr^2
A = π(40 cm)^2
A = 1600π cm^2
Since the larger cake has an area of 1600π cm^2, we can divide this by the area per person (100π cm^2) to find out how many people it will feed:
Number of people = Area of larger cake / Area per person
Number of people = 1600π cm^2 / 100π cm^2
Number of people = 16
Therefore, an 80 cm diameter cake will feed 16 people.
A = pi * r^2
A = 3.14 * 20^2
A = 1256 sq. cm
1256 / 4 = 314 sq. cm per person
Do the same for the larger cake.