A cone is a 3-dimensional shape that consists of a circular or flat surface and a curved side. Thus the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]
A cone is a 3-dimensional shape that consists of a circular or flat surface and curved side. Its volume can be determined by;
The volume of a cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius of its flat surface, and h is its height.
From the given question, we have to determine the value of h using the Pythagoras theorem.
Such that;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]4^{2}[/tex] = [tex]h^{2}[/tex] + [tex]1^{2}[/tex]
16 = [tex]h^{2}[/tex] + 1
[tex]h^{2}[/tex] = 15
h = [tex]\sqrt{15}[/tex]
Thus the volume of the cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\frac{1}{3}[/tex]x [tex]\frac{22}{7}[/tex] x [tex]1^{2}[/tex]x [tex]\sqrt{15}[/tex]
= 4.0574
Therefore the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]
For more clarifications on the volume of a cone, visit: https://brainly.com/question/26936929
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