Question

Konery wants to make their waffle cones with a height of 6 in. Their current net design has a diameter of 2.5 in. and a slant height of 6.25 in. Will this work for the desired height? Round the answer to the nearest tenth.(1 point) Responses No, the height is too long by 0.4 in. No, the height is too long by 0.4 in. No, the height is too long by 0.1 in. No, the height is too long by 0.1 in. No the height is too short by 0.3 in. No the height is too short by 0.3 in. No, the height is too long by 0.7 in.

Answer 1

To determine whether the current design will work for the desired height, we can use the relationship between the slant height, radius, and height of a cone.

Given:
- Diameter = 2.5 inches → Radius \( r = \frac{2.5}{2} = 1.25 \) inches
- Slant height \( l = 6.25 \) inches
- Desired height \( h = 6 \) inches

The relationship between the slant height \( l \), height \( h \), and radius \( r \) of a cone is given by the Pythagorean theorem:

\[ l^2 = r^2 + h^2 \]

Now substituting the known values:

1. Calculate \( r^2 \):
\[
r^2 = (1.25)^2 = 1.5625
\]

2. Calculate \( l^2 \):
\[
l^2 = (6.25)^2 = 39.0625
\]

3. Set up the equation:
\[
39.0625 = 1.5625 + h^2
\]

4. Solve for \( h^2 \):
\[
h^2 = 39.0625 - 1.5625 = 37.5
\]

5. Now, find \( h \):
\[
h = \sqrt{37.5} \approx 6.123
\]

Now we can find the difference between the calculated height and the desired height:

\[
\text{Difference} = 6.123 - 6 = 0.123 \text{ inches}
\]

Rounding this to the nearest tenth gives 0.1 inches. Since the calculated height is slightly greater than the desired height of 6 inches, we can conclude:

**No, the height is too long by 0.1 in.**