Question

The answer to this question Volume =9,145.33 pi in^3 Diameter =38

Answer 1

Answer: $diameter=38\ in$

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:

$V=\frac{4}{3}\pi r^3$

Where "r" is the radius.

2. The radius is twice the diameter.

So, knowing that the volume of the sphere is:

$V=9,145.33\pi\ in^3$

You can substitute them into the equation and then solve for "r" in order to find its value:

$9,145.33\pi\ in^3=\frac{4}{3}\pi r^3\\\\\frac{(3)(9,145.33\pi\ in^3)}{4\pi}=r^3\\\\\sqrt[3]{\frac{(3)(9,145.33\pi\ in^3)}{4\pi}}=r\\\\r=19\ in$

Then, the diameter is:

$d=2r\\\\d=2(19\ in)\\\\d=38\ in$