QQuestionMathematics
QuestionMathematics
MODELING WITH MATHEMATICS The radius $r$ of the base of a cone is given by the equation $r=\left(\frac{3 V}{\pi h}\right)^{1 / 2}$, where $V$ is the volume of the cone and $h$ is the height of the cone. Find the radius of the paper cup to the nearest inch. Use 3.14 for $\pi$.
The radius is about $\square$ inch(es).
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Answer
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Step 1:I'll solve this step by step using the given equation and the LaTeX formatting guidelines:
Step 2:: Identify the given information
- Equation for radius: $$r = \left(\frac{3V}{\pi h}\right)^{1/2}
- Use \pi = 3.14 - We need to find the radius of the paper cup
Step 3:: Determine the volume (V) and height (h)
From the image, I can see: - Volume (V) = 9 cubic inches - Height (h) = 6 inches
Step 4:: Substitute the values into the equation
r = \left(\frac{3 \cdot 9}{3.14 \cdot 6}\right)^{1/2}
Step 5:: Simplify inside the parentheses
r = \left(\frac{27}{18.84}\right)^{1/2}
Step 6:: Divide inside the parentheses
r = \left(1.433\right)^{1/2}
Step 7:: Calculate the square root
r = 1.197
Step 8:: Round to the nearest inch
r \approx 1
Final Answer
The radius of the paper cup is 1 inch.
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