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 short by 0.3 in.
No; the height is too short by 0.3 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 long by 0.4 in.
No; the height is too long by 0.4 in.

No; the height is too long by 0.7 in. 

Answer 1

To determine whether the current net design will work for a waffle cone with a desired height of 6 inches, we can use the relationship between the cone's slant height, radius, and height.

Given:
- Desired height (h) = 6 inches
- Diameter (d) = 2.5 inches
- Radius (r) = d/2 = 2.5/2 = 1.25 inches
- Slant height (l) = 6.25 inches

We can use the Pythagorean theorem to find the relationship between the height (h), radius (r), and slant height (l) of a cone:

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

Now we will substitute the known values into this equation:

\[
6.25^2 = h^2 + (1.25)^2
\]

Calculating \(6.25^2\) and \((1.25)^2\):

\[
39.0625 = h^2 + 1.5625
\]

Now, we can solve for \(h^2\):

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

Taking the square root can give us the height h:

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

Now, we check how this height compares to the desired height of 6 inches:

\[
6.123 - 6 = 0.123
\]

Thus, the current height is approximately 0.123 inches longer than the desired height of 6 inches.

When rounding to the nearest tenth:

0.123 rounds to 0.1.

So the answer is:

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