Let's call the original height of the cylinder h1 and the diameter d1. We can set up a proportion to solve for the new diameter d2:
h1/d1 = h2/d2
We know h1 = 27 cm (since 54/2 = 27) and h2 = 40.5 cm. We want to solve for d2.
Substituting in the values we know:
27/d1 = 40.5/d2
Cross-multiplying:
27d2 = 40.5d1
Solving for d2:
d2 = (40.5d1)/27
We don't know d1, but we can solve for it using the information given in the answer choices.
If we try answer choice A, d1 = 30 cm:
d2 = (40.5 * 30) / 27 = 45 cm
This doesn't match any of the answer choices, so it's not the correct answer.
If we try answer choice B, d1 = 12 cm:
d2 = (40.5 * 12) / 27 = 18 cm
This matches answer choice D, so the correct answer is D, 18 cm.