A bakery offers a small circular cake with a diameter of 8 inches. It also offers a large circular cake with a diameter of
24 inches. Does the top of the large cake have three times the area of that of the small cake? If not, how much greater is
its area? Explain.
Area of top cake: ______________
Area of bottom cake: ______________
Answer: Yes / No
Explanation: _________________________________________________________
____________________________________________________________________
_____________________________________
I'll be glad to check your answers.
Na bruh, it doesnt. Area of small: 50.3
Area of big: 452.4
50.3*3 doesnt equal 452.4
To determine if the top of the large cake has three times the area of the small cake, we need to calculate the areas of both cakes.
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius.
For the small cake with a diameter of 8 inches, the radius (r) would be half of the diameter, which is 8/2 = 4 inches.
Therefore, the area of the small cake is A_small = π(4^2) = 16π square inches.
For the large cake with a diameter of 24 inches, the radius (r) would be half of the diameter, which is 24/2 = 12 inches.
Therefore, the area of the large cake is A_large = π(12^2) = 144π square inches.
Now, let's compare the areas:
The area of the top small cake is 16π square inches.
The area of the top large cake is 144π square inches.
To determine whether the top of the large cake has three times the area of the small cake, we can divide the area of the large cake by the area of the small cake:
144π / 16π = 9
Therefore, the top of the large cake has 9 times the area of the small cake, not three times.
Explanation:
The area of a circle is proportional to the square of its radius. Since the radius of the large cake is three times the radius of the small cake (12 inches / 4 inches), the area of the large cake is nine times the area of the small cake (12^2 / 4^2 = 144 / 16 = 9).
To determine whether the top of the large cake has three times the area of the small cake or not, we need to calculate the areas of both cakes.
First, let's calculate the area of the small cake with a diameter of 8 inches. The formula to find the area of a circle is A = πr^2, where A represents the area and r represents the radius.
Given the diameter is 8 inches, the radius is half of the diameter, which is 8/2 = 4 inches. Plugging this value into the formula, we get:
A_small = π * 4^2 = π * 16 ≈ 50.27 square inches
Next, let's calculate the area of the large cake with a diameter of 24 inches. Using the same formula, we find the radius is 24/2 = 12 inches. Plugging this value into the formula:
A_large = π * 12^2 = π * 144 ≈ 452.39 square inches
Now we can compare the two areas:
A_large / A_small = 452.39 / 50.27 ≈ 8.99
The ratio of the area of the large cake to the small cake is approximately 8.99. Therefore, the top of the large cake does not have three times the area of the small cake. However, the area of the large cake is approximately 8.99 times greater than the area of the small cake.
Area of top cake: 452.39 square inches
Area of bottom cake: 50.27 square inches
Answer: No
Explanation: The area of the top cake is approximately 8.99 times greater than the area of the bottom cake.