The volume of container M can be calculated using the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we have:
V = π(3 in)^2(9.5 in)
V ≈ 254.47 cubic inches
Let x be the volume of one box of sugar. According to the problem, the cook emptied one box of sugar into the container, and then added some fraction of another box to completely fill it. This means that the total volume of sugar added is equal to 1 + some fraction of x.
We can set up an equation to solve for x:
1 + (1/n)x = 254.47
where n is the fraction of the second box of sugar added.
Solving for x, we get:
x = (254.47 - 1) n
x = 253.47n
To find the value of n, we can subtract 1 box of sugar from the total volume added, and then divide by the volume of one box:
n = (254.47 - 1) / x
n = 253.47 / x
Substituting the expression for x from above, we get:
n = 253.47 / (253.47n)
n^2 = 253.47 / 1
n ≈ 15.93
Therefore, the volume of one box of sugar is approximately:
x ≈ 253.47 / 15.93
x ≈ 15.91 cubic inches