Question

14 of 15 14 of 15 Items 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.

Answer 1

To determine if the current net design of the waffle cone will work for a desired height of 6 inches, we need to check the relationship between the slant height, the height, and the radius of the cone.

The slant height (l), height (h), and radius (r) of a cone are related by the Pythagorean theorem:

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

Given:
- Desired height \( h = 6 \) inches
- Diameter \( d = 2.5 \) inches, so the radius \( r = \frac{d}{2} = \frac{2.5}{2} = 1.25 \) inches
- Current slant height \( l = 6.25 \) inches

Now we can substitute these values into the Pythagorean theorem equation to see if they are consistent:

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

2. Calculate \( h^2 \):
\[
h^2 = (6)^2 = 36
\]

3. Now add \( r^2 \) and \( h^2 \):
\[
r^2 + h^2 = 1.5625 + 36 = 37.5625
\]

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

Now we compare \( l^2 \) and \( r^2 + h^2 \):
- \( r^2 + h^2 = 37.5625 \)
- \( l^2 = 39.0625 \)

Since \( l^2 \) (39.0625) is greater than \( r^2 + h^2 \) (37.5625), the relationship holds true, meaning that a cone with these dimensions can have a height of 6 inches and a slant height of 6.25 inches.

Therefore, **the current net design will work for the desired height** of 6 inches.