Answer: [tex]diameter=38\ in[/tex]
Step-by-step explanation:
Based on the picture I assume that the exercise asks for the diameter of the sphere.
So, it is necessary to remember the following:
1. the volume of a sphere can be calculated with the following formula:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where "r" is the radius.
2. The radius is twice the diameter.
So, knowing that the volume of the sphere is:
[tex]V=9,145.33\pi\ in^3[/tex]
You can substitute them into the equation and then solve for "r" in order to find its value:
[tex]9,145.33\pi\ in^3=\frac{4}{3}\pi r^3\\\\\frac{(3)(9,145.33\pi\ in^3)}{4\pi}=r^3\\\\\sqrt[3]{\frac{(3)(9,145.33\pi\ in^3)}{4\pi}}=r\\\\r=19\ in\\\\[/tex]
Then, the diameter is:
[tex]d=2r\\\\d=2(19\ in)\\\\d=38\ in[/tex]
