To determine if the waffle cone design will work for the desired height of 6 inches, we can use the relationship between the height (h), slant height (l), and radius (r) of the cone, which is given by the Pythagorean theorem:
\[ l^2 = r^2 + h^2 \]
- First, we need to find the radius from the diameter. The diameter is given as 2.5 inches, thus the radius (r) is:
\[ r = \frac{d}{2} = \frac{2.5}{2} = 1.25 , \text{inches} \]
- We know the slant height (l) is 6.25 inches. Now we can set up the equation to find the height (h):
\[ l^2 = r^2 + h^2 \]
Plugging in the values:
\[ 6.25^2 = 1.25^2 + h^2 \]
Calculating the squares:
\[ 39.0625 = 1.5625 + h^2 \]
Now, solving for \( h^2 \):
\[ h^2 = 39.0625 - 1.5625 \] \[ h^2 = 37.5 \]
Taking the square root to find the height:
\[ h = \sqrt{37.5} \approx 6.123 , \text{inches} \]
- Now we compare this height with the desired height of 6 inches:
\[ 6.123 - 6 = 0.123 , \text{inches} \]
This means the height is too long by approximately 0.1 inches when rounded to the nearest tenth.
Therefore, the final answer is: No; the height is too long by 0.1 in.