Answer: Let's call the scale factor between the two containers "k". Then, we know that the ratio of their surface areas is equal to the square of the scale factor:
(surface area of B) / (surface area of A) = k^2
We also know that the ratio of their volumes is equal to the cube of the scale factor:
(volume of B) / (volume of A) = k^3
We can rearrange the first equation to solve for k:
k^2 = (surface area of B) / (surface area of A) = 10478 mm^2 / 1550 mm^2 = 6.75
Taking the square root of both sides, we get:
k = sqrt(6.75) = 2.6 (rounded to one decimal place)
Now we can use the second equation to find the volume of container A:
(volume of B) - (volume of A) = 62160 mm^3
(k^3)(volume of A) - (volume of A) = 62160 mm^3
Simplifying and solving for the volume of A, we get:
volume of A = 62160 mm^3 / (k^3 - 1) = 62160 mm^3 / (2.6^3 - 1) ≈ 4477 mm^3
Therefore, the volume of container A is approximately 4477 mm^3.
Explanation: