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Mario says he found the height of a cone that has a volume of 72 cubic millimeters and a diameter of 12 millimeters. 72π = 1 3 π(12²)h 1. 72π = 1 3 π(144)h 2. 72π = 48π(h) 3. 1.5 = h Analyze Mario’s work. Is he correct? If not, what was his mistake? a. Yes, he is correct. b. No, he did not correctly square 12 on the left side. c. No, he did not use the radius measure in the formula. d. No, he did not correctly undo the multiplication on the right side.

User Brilliant
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2 Answers

3 votes

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)

User Foxwendy
by
8.6k points
4 votes

Answer:

C) No, he did not use the radius measure in the formula.

Proof:

Mario says he found the height of a cone that has a volume of 72 cubic millimeters-example-1
User Kumba
by
8.3k points
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