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 0.1 in.
No; the height is too long by 0.1 in.

No; the height is too long by 0.7 in. 
No; the height is too long by 0.7 in. 

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 short by 0.3 in.

Answer 1

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:

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

1. First, we need to find the radius from the diameter. The diameter is given as 2.5 inches, thus the radius (r) is:

\[ r = \frac{d}{2} = \frac{2.5}{2} = 1.25 \, \text{inches} \]

2. 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:

\[ h = \sqrt{37.5} \approx 6.123 \, \text{inches} \]

3. 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.**