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)

Question

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 if the current design will work for the desired height, we can use the relationship between the cone's height, radius, and slant height. Specifically, we can use the Pythagorean theorem.

1. The radius of the cone is half the diameter: \[ \text{Radius} = \frac{2.5 \text{ in}}{2} = 1.25 \text{ in} \]

2. We'll let \( h \) represent the height of the cone, and we know the slant height \( l \) is 6.25 in. According to the Pythagorean theorem: \[ l^2 = r^2 + h^2 \]

3. Plugging in the values: \[ (6.25)^2 = (1.25)^2 + h^2 \] \[ 39.0625 = 1.5625 + h^2 \] \[ h^2 = 39.0625 - 1.5625 \] \[ h^2 = 37.5 \]

4. Now taking the square root of both sides: \[ h = \sqrt{37.5} \approx 6.123 \]

5. Rounding this to the nearest tenth gives: \[ h \approx 6.1 \text{ in} \]

Now, we need to compare this height with the desired height of 6 in:

• The current height (6.1 in) is longer than the desired height (6 in).

To find out how much longer it is: \[ 6.1 \text{ in} - 6 \text{ in} = 0.1 \text{ in} \]

Since the current height is longer than the desired height by 0.1 in, the correct response is: No, the height is too long by 0.1 in.