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 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.
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 0.7 in. 

Answer 1

To determine whether the waffle cone design will meet the desired height, we can use the relationship between the slant height, radius (half of the diameter), and the height of the cone.

1. The radius (r) can be calculated as half of the diameter:

   • Diameter = 2.5 in., so radius \( r = \frac{2.5}{2} = 1.25 \) in.

2. The slant height (l) is given as 6.25 in.

3. The height (h) can be calculated using the Pythagorean theorem, where: \[ l^2 = r^2 + h^2 \] Rearranging gives: \[ h^2 = l^2 - r^2 \] Solving for h gives: \[ h = \sqrt{l^2 - r^2} \]

4. Plugging in the values: \[ l = 6.25 , \text{in}, , r = 1.25 , \text{in} \] \[ h = \sqrt{(6.25)^2 - (1.25)^2} \] \[ h = \sqrt{39.0625 - 1.5625} = \sqrt{37.5} \] \[ h \approx 6.123 , \text{in} \]

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

6. Finally, we compare the calculated height to the desired height: \[ 6.1 , \text{in} , \text{(calculated height)} \text{ is greater than } 6 , \text{in} , \text{(desired height)} \] The height is too long by: \[ 6.1 , \text{in} - 6 , \text{in} = 0.1 , \text{in} \]

Thus, the correct response is: No; the height is too long by 0.1 in.