Since the cone has a volume of 37.68 cubic yards, the slant height of the cone is equal to 25 yards.
Given the following data:
Volume of cone = 37.68 cubic yards
Diameter of cone = 6 yards.
Radius of cone = [tex]\frac{6}{2}[/tex] = 3 yards.
Mathematically, the volume of a cone is given by this formula:
[tex]V = \frac{1}{3} \pi r^2\sqrt{(l^2-r^2)}[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]37.68 = \frac{1}{3} \times \pi 3^2\sqrt{(l^2-3^2)}\\\\37.68 =9.426\sqrt{(l^2-9)}\\\\1419.78=88.85(l^2-9)\\\\1419.78=88.85l^2-799.65\\\\88.85l^2=1419.78+799.65\\\\l=\sqrt{\frac{2219.43}{88.85} }[/tex]
l = 24.98 ≈ 25 yards.
Read more on radius here: brainly.com/question/21367171
