Answer: First option.
Step-by-step explanation:
The formula that is used to calculate the volume of a cone is:
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Where "V" is the volume, "r" is the radius and "h" is the height.
In this case we know that we must used 3.14 for [tex]\pi[/tex], and:
[tex]V=29.31\ in^3\\\\h=7\ in[/tex]
Then, we can substitute values into the formula:
[tex]29.31=\frac{1}{3}(3.14)r^2(7)[/tex]
Now we must solve for "r":
[tex]29.31=\frac{1}{3}(3.14)r^2(7)\\\\\frac{3(29.31)}{(3.14)(7)}=r^2\\\\\sqrt{\frac{3(29.31)}{(3.14)(7)}}=r\\\\r=2\ in[/tex]
Since the diameter is twice the radius, we get that the diameter of the cone is:
[tex]d=2(2\ in)\\\\d=4\ in[/tex]
