To determine if the current design will work for the desired height of 6 inches, we can use the dimensions of the cone: the slant height, the radius, and the height.
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Calculate the radius: The diameter is given as 2.5 inches, so the radius \( r \) is: \[ r = \frac{2.5}{2} = 1.25 \text{ inches} \]
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Slant height: The slant height \( s \) is given as 6.25 inches.
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Use the Pythagorean theorem to find the height \( h \) of the cone: \[ s^2 = r^2 + h^2 \] Plugging in our known values: \[ 6.25^2 = 1.25^2 + h^2 \] Calculate \( 6.25^2 \) and \( 1.25^2 \): \[ 39.0625 = 1.5625 + h^2 \] Now, solve for \( h^2 \): \[ h^2 = 39.0625 - 1.5625 = 37.5 \] Taking the square root to find \( h \): \[ h = \sqrt{37.5} \approx 6.123 \text{ inches} \]
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Determine if this height meets the requirement: The desired height is 6 inches. \[ h \approx 6.1 \text{ inches} \]
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Calculate the difference: \[ \text{Difference} = 6.1 - 6 = 0.1 \text{ inches} \]
Since the actual height is greater than the desired height by approximately 0.1 inches, the response is:
No; the height is too long by 0.1 in.
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