Question

Triangles Online Practice
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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 if Konery's waffle cone design will work, we need to calculate the actual height of the cone using the given slant height and radius.

1. **Find the radius of the cone:**
The diameter of the cone is 2.5 inches, so the radius (r) is:
\[
r = \frac{2.5}{2} = 1.25 \text{ inches}
\]

2. **Use the Pythagorean theorem to find the height (h) of the cone:**
In a cone, the slant height (l), height (h), and radius (r) form a right triangle:
\[
l^2 = r^2 + h^2
\]

Plugging in the values:
\[
(6.25)^2 = (1.25)^2 + h^2
\]

\[
39.0625 = 1.5625 + h^2
\]

\[
h^2 = 39.0625 - 1.5625 = 37.5
\]

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

3. **Calculate the difference in height:**
The desired height is 6 inches. The calculated height is approximately 6.1 inches.
\[
\text{Difference} = 6.123 - 6 = 0.123 \text{ inches}
\]

Rounding 0.123 inches to the nearest tenth gives approximately 0.1 inches.

4. **Conclusion:**
Since the actual height is 0.1 inches taller than the desired height of 6 inches, the correct response is:

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