Question

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 short by 0.3 in
No; the height is too short by 0.3 in

No; the height is too long by 0.4 in

Answer 1

To determine if the current design will work for the desired height of 6 inches, we can use the dimensions of the cone: the slant height, the radius, and the height.

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

2. **Slant height**: The slant height \( s \) is given as 6.25 inches.

3. **Use the Pythagorean theorem** to find the height \( h \) of the cone:
\[
s^2 = r^2 + h^2
\]
Plugging in our known values:
\[
6.25^2 = 1.25^2 + h^2
\]
Calculate \( 6.25^2 \) and \( 1.25^2 \):
\[
39.0625 = 1.5625 + h^2
\]
Now, solve for \( h^2 \):
\[
h^2 = 39.0625 - 1.5625 = 37.5
\]
Taking the square root to find \( h \):
\[
h = \sqrt{37.5} \approx 6.123 \text{ inches}
\]

4. **Determine if this height meets the requirement**: The desired height is 6 inches.
\[
h \approx 6.1 \text{ inches}
\]

5. **Calculate the difference**:
\[
\text{Difference} = 6.1 - 6 = 0.1 \text{ inches}
\]

Since the actual height is greater than the desired height by approximately 0.1 inches, the response is:

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