Question

triangles online practice
complete this assessment to review what youve learned. it will not count toward your grade.
konery wants to make waffle cones with a height of 6 in. her 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
earest tenth. (1 point)
no; the height is too long by 0.4 in.
no; the height is too long by 0.7 in.
no; the height is too long by 0.1 in.
no; the height is too short by 0.3 in.

Explanation:

Step1: Find the radius

The diameter \(d = 2.5\) in, so the radius \(r=\frac{d}{2}=\frac{2.5}{2}=1.25\) in.

Step2: Use the Pythagorean theorem for the cone

For a cone, \(l^{2}=h^{2}+r^{2}\), where \(l\) is the slant height, \(h\) is the height and \(r\) is the radius. We want to find \(h\), so \(h=\sqrt{l^{2}-r^{2}}\).
Substitute \(l = 6.25\) in and \(r = 1.25\) in: \(h=\sqrt{6.25^{2}-1.25^{2}}=\sqrt{(6.25 + 1.25)(6.25-1.25)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\))
\(=\sqrt{7.5\times5}=\sqrt{37.5}\approx6.1\) in.

Step3: Calculate the difference

The desired height is \(6\) in. The difference is \(6.1-6=0.1\) in.

Answer:

No; the height is too long by \(0.1\) in.