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.
Step 3:: Simplify the right side of the equation.
First, cancel out the $$\pi$$ terms: $$48 = \frac{1}{3} r^{2} (36)$$.
Next, simplify the fraction and the expression in parentheses: 48 = r^{2} (12).
Step 4:: Divide both sides by 12 to isolate r^{2}: \frac{48}{12} = r^{2}.
This simplifies to $$4 = r^{2}$$.
Step 5:: Take the square root of both sides to find the value of r.
However, since the radius cannot be negative, we take only the positive square root: $$r = \sqrt{4} = 2$$.
Remember that there are two possible solutions, one positive and one negative.
Final Answer
The radius of the cone is 2 inches.
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