To determine whether the current net design will work for a waffle cone with a desired height of 6 inches, we can use the relationship between the cone's slant height, radius, and height.
Given:
- Desired height (h) = 6 inches
- Diameter (d) = 2.5 inches
- Radius (r) = d/2 = 2.5/2 = 1.25 inches
- Slant height (l) = 6.25 inches
We can use the Pythagorean theorem to find the relationship between the height (h), radius (r), and slant height (l) of a cone:
\[ l^2 = h^2 + r^2 \]
Now we will substitute the known values into this equation:
\[ 6.25^2 = h^2 + (1.25)^2 \]
Calculating \(6.25^2\) and \((1.25)^2\):
\[ 39.0625 = h^2 + 1.5625 \]
Now, we can solve for \(h^2\):
\[ h^2 = 39.0625 - 1.5625 = 37.5 \]
Taking the square root can give us the height h:
\[ h = \sqrt{37.5} \approx 6.123 \]
Now, we check how this height compares to the desired height of 6 inches:
\[ 6.123 - 6 = 0.123 \]
Thus, the current height is approximately 0.123 inches longer than the desired height of 6 inches.
When rounding to the nearest tenth:
0.123 rounds to 0.1.
So the answer is:
No; the height is too long by 0.1 in.