A cake shop offers circular cakes with diameters of 8 in., 12 in., and 15in. Identify the area of each cake rounded to the nearest tenth.
A. A1 = 25.1 in2; A2 = 37.7 in2; A3 = 47.1 in2
B. A1 = 12.6 in2; A2 = 18.8 in2; A3 = 23.6 in2
C. A1 = 201.1 in2; A2 = 452.4 in2; A3 = 706.9 in2
D. A1 = 50.3 in2; A2 = 113.1 in2; A3 = 176.7 in2
alright thanks.
To find the area of a circular cake, we use the formula A = πr^2, where A is the area and r is the radius of the cake.
The diameter of a cake is twice the length of the radius. Therefore, we can find the radius by dividing the diameter by 2.
Let's calculate the area of each cake:
For the cake with a diameter of 8 inches:
- The radius is 8/2 = 4 inches.
- Plugging the radius into the formula, A = π(4)^2 = 16π. Rounded to the nearest tenth, this is approximately 50.3 square inches.
For the cake with a diameter of 12 inches:
- The radius is 12/2 = 6 inches.
- Plugging the radius into the formula, A = π(6)^2 = 36π. Rounded to the nearest tenth, this is approximately 113.1 square inches.
For the cake with a diameter of 15 inches:
- The radius is 15/2 = 7.5 inches.
- Plugging the radius into the formula, A = π(7.5)^2 = 56.25π. Rounded to the nearest tenth, this is approximately 176.7 square inches.
Therefore, the area of each cake, rounded to the nearest tenth, is:
A. A1 = 25.1 in^2; A2 = 37.7 in^2; A3 = 47.1 in^2
To calculate the area of a circular cake, you need to use the formula for the area of a circle, which is A = πr², where A represents the area and r represents the radius.
Given the diameter of each cake, you can find the radius by dividing the diameter by 2. Once you have the radius, substituting it into the formula will give you the area.
Let's calculate the area for each cake:
For the first cake with a diameter of 8 inches:
- The radius is 8/2 = 4 inches.
- Substituting the radius into the formula, we have A = π(4)² ≈ 3.14 * 16 = 50.24 in².
- Rounded to the nearest tenth, the area is approximately 50.3 in².
For the second cake with a diameter of 12 inches:
- The radius is 12/2 = 6 inches.
- Substituting the radius into the formula, we have A = π(6)² ≈ 3.14 * 36 = 113.04 in².
- Rounded to the nearest tenth, the area is approximately 113.1 in².
For the third cake with a diameter of 15 inches:
- The radius is 15/2 = 7.5 inches.
- Substituting the radius into the formula, we have A = π(7.5)² ≈ 3.14 * 56.25 ≈ 176.625 in².
- Rounded to the nearest tenth, the area is approximately 176.7 in².
So, the correct answer is:
D. A1 = 50.3 in²; A2 = 113.1 in²; A3 = 176.7 in².
Formula for area of circle is:
A = π * r ^ 2
So, you'll want to calculate the area of each cake and see which answer contains your areas rounded to the nearest tenth.