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 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.