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)

To determine if the waffle cone design will work for the desired height, we can compare the actual height of the cone based on the given slant height (6.25 inches) and diameter (2.5 inches) to the desired height (6 inches).

The cone's radius \( r \) is half of the diameter: \[ r = \frac{2.5}{2} = 1.25 \text{ in.} \]

Using the Pythagorean theorem, we can find the actual height \( h \) of the cone. The relationship between the height, radius, and slant height of a cone is given by: \[ s^2 = r^2 + h^2 \] where \( s \) is the slant height.

Plugging in the values: \[ (6.25)^2 = (1.25)^2 + h^2 \] \[ 39.0625 = 1.5625 + h^2 \] Subtracting \( 1.5625 \) from both sides gives: \[ h^2 = 39.0625 - 1.5625 \] \[ h^2 = 37.5 \] Now, take the square root of both sides to find \( h \): \[ h = \sqrt{37.5} \approx 6.123 \text{ in.} \]

Now, we compare this to the desired height of 6 inches: \[ 6.123 - 6 = 0.123 \text{ in.} \]

Since \( h \approx 6.1 \text{ in.} \) is more than 6 in., we round the difference to the nearest tenth: \[ 0.1 \text{ in.} \]

Thus, we conclude that the height is too long by approximately \( 0.1 \text{ in.} \)

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