QQuestionMathematics
QuestionMathematics
The volume of a cone is 48π cubic inches. The cone has a height of 36 inches. Mark is finding the radius of the cone. Complete his work. 1. Rewrite the formula including the area of the base: 2. Substitute the values into the formula: 3. Simplify the right side: 4. Divide 12π to both sides: Step 5 is to . The radius of the cone is . V = 1 3 πr²h 48π = 1 3 πr²(36) 48π = 12πr² 4 = r²
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Answer
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Step 1: Recognize that the formula for the volume of a cone is given by V = \frac{1}{3} \pi r^{2} h, where V represents the volume, r represents the radius of the base, and h represents the height.
Mark has already written this formula as $$V = \frac{1}{3} \pi r^{2} h$$.
Step 2: Substitute the given values into the formula.
Thus, we have $$48\pi = \frac{1}{3} \pi r^{2} (36)$$.
The problem states that the volume is 48π cubic inches and the height is 36 inches.
Final Answer
The radius of the cone is 2 inches.
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