Bot GPT 4-o mini To determine if Konery's waffle cone design will work, we need to calculate the actual height of the cone using the given slant height and radius.
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Find the radius of the cone: The diameter of the cone is 2.5 inches, so the radius (r) is: \[ r = \frac{2.5}{2} = 1.25 \text{ inches} \]
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Use the Pythagorean theorem to find the height (h) of the cone: In a cone, the slant height (l), height (h), and radius (r) form a right triangle: \[ l^2 = r^2 + h^2 \]
Plugging in the values: \[ (6.25)^2 = (1.25)^2 + h^2 \]
\[ 39.0625 = 1.5625 + h^2 \]
\[ h^2 = 39.0625 - 1.5625 = 37.5 \]
\[ h = \sqrt{37.5} \approx 6.123 \text{ inches} \]
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Calculate the difference in height: The desired height is 6 inches. The calculated height is approximately 6.1 inches. \[ \text{Difference} = 6.123 - 6 = 0.123 \text{ inches} \]
Rounding 0.123 inches to the nearest tenth gives approximately 0.1 inches.
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Conclusion: Since the actual height is 0.1 inches taller than the desired height of 6 inches, the correct response is:
No; the height is too long by 0.1 in.
1 answer