To determine if the current net design will work for the desired height of 6 inches, we need to calculate the vertical height of the cone using the slant height and the radius.
The slant height (l) of the cone is given as 6.25 inches, and the diameter is 2.5 inches, which means the radius (r) is half of the diameter:
\[ r = \frac{2.5}{2} = 1.25 \text{ inches} \]
We can use the Pythagorean theorem to find the vertical height (h) of the cone. The relationship is given by:
\[ l^2 = r^2 + h^2 \]
Substituting the known values:
\[ (6.25)^2 = (1.25)^2 + h^2 \]
Calculating \( (6.25)^2 \) and \( (1.25)^2 \):
\[ 39.0625 = 1.5625 + h^2 \]
Now, solve for \( h^2 \):
\[ h^2 = 39.0625 - 1.5625 \] \[ h^2 = 37.5 \]
Taking the square root to find h:
\[ h = \sqrt{37.5} \]
Calculating the square root:
\[ h \approx 6.123 \text{ inches} \]
Now, we compare the calculated height with the desired height of 6 inches:
The difference is:
\[ 6.123 - 6 = 0.123 \text{ inches} \]
Rounding to the nearest tenth, we find:
0.1 inches
So the answer is:
No; the height is too long by 0.1 in.