Answer:
h = 6 is the correct answer.
Explanation:
To find the height (h) of a cone with volume V and diameter d, we can use the formula:
V = (1/3)πr^2h, where r is the radius of the cone and d = 2r.
In this problem, we are given that the volume V = 72 cubic millimeters and the diameter d = 12 millimeters. Therefore, the radius r = d/2 = 6 millimeters.
Substituting these values into the formula, we get:
72π = (1/3)π(6^2)h
72π = 12πh
h = 6
So, the correct answer is h = 6, which means that Mario's work is incorrect.
Looking at Mario's work, he correctly wrote down the formula for the volume of a cone and substituted the given values, but he made a mistake in simplifying the equation.
On the left side of the equation, he correctly multiplied 72 by π, but he should have divided the result by 3 to get (1/3)π(144), instead of π(144).
On the right side of the equation, he correctly wrote down the product of (1/3)π(12^2) and h, but he simplified it incorrectly by multiplying 48π by h instead of 12π by h.
Therefore, the correct equation after simplification would be:
(1/3)π(144)h = 72π
Simplifying this equation further would give us h = 6, which is the correct answer.
(Reference to Chatgpts work)