Final answer:
To find the ratio of the diameter of the large butter cake to the diameter of the small butter cake, we need to find the ratio of the areas of the large and small cakes.
Step-by-step explanation:
To find the ratio of the diameter of the large butter cake to the diameter of the small butter cake, we can use the fact that the ratio of the areas of two similar shapes is equal to the square of the ratio of their corresponding side lengths. In this case, the corresponding dimensions are the diameters of the cakes. So, we need to find the ratio of the areas of the large and small cakes.
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Since the diameter is twice the radius, we can rewrite the formula as A = π(d/2)^2, where d is the diameter of the circle.
Let's calculate the areas of the large and small cakes using their given masses:
The mass of the large cake = 250 g
diameter of the large cake = ?
The mass of the small cake = 54 g
diameter of the small cake = ?