Rachel is frosting the top of two cakes and wants to know which cake will require more frosting. one cake is round with a diameter of 8 inches. the other cake a square with the length of 9 inches. the top of which cake has a larger area? how much larger is it?
circle: A = pi * r^2
square: A = 4s
Just plug in the numbers
so A=8 r^2 and
A=9s
The radius is not 8. The diameter is 8. What happened to pi?
A = 4s
A=pi times r squared=3.14 times 4x4 = 50.265
Do a search for area of a circle and you'll find a great site for solving geometry problems.
it should be obvious that the square is larger, since the circle fits inside it
but by how much?
circle: 16 pi = 50.26
square: 9^2 = 81
.
To determine which cake requires more frosting, we need to compare the areas of the tops of the cakes.
1. For the round cake:
The area of a circle is calculated using the formula A = πr^2, where "A" is the area and "r" is the radius. Since we are given the diameter, which is 8 inches, we can find the radius by dividing the diameter by 2: r = 8/2 = 4 inches.
Now we can calculate the area: A = π(4^2) = 16π square inches.
2. For the square cake:
The area of a square is calculated by multiplying the length of one side by itself. In this case, the length of one side is given as 9 inches, so the area of the square cake is A = 9 * 9 = 81 square inches.
Now we can compare the two areas:
The area of the round cake = 16π square inches.
The area of the square cake = 81 square inches.
To find out which cake has a larger area, we can compare the numerical values of the areas:
16π vs. 81
Since π (pi) is approximately 3.14, we can find an approximation for the area of the round cake:
16π ≈ 16 * 3.14 ≈ 50.24 square inches.
Comparing 50.24 with 81, we can conclude that the square cake has a larger area.
To find out how much larger it is, we can subtract the area of the round cake from the area of the square cake:
81 - 50.24 ≈ 30.76 square inches.
Therefore, the square cake has an area that is approximately 30.76 square inches larger than the round cake.