Find the volume of the sphere below inscribed in a cube with an edge length of 4 units. Round your answer to the nearest hundredth if necessary cubic units

To find the volume of a sphere inscribed in a cube, you first need to know that the diameter of the sphere is equal to the edge length of the cube. In this case, the edge length of the cube is 4 units.

1. Find the radius of the sphere:

The radius (r) is half of the diameter.

[ r = frac{4}{2} = 2 text{ units} ]

2. Use the formula for the volume of a sphere:

The formula for the volume (V) of a sphere is:

[ V = frac{4}{3} pi r^3 ]

3. Plug in the radius:

[ V = frac{4}{3} pi (2)^3 ]

[ V = frac{4}{3} pi (8) ]

[ V = frac{32}{3} pi ]

4. Approximate using ( pi approx 3.14 ):

[ V approx frac{32}{3} times 3.14 ]

[ V approx 33.51 text{ cubic units} ]

So, the volume of the sphere is approximately 33.51 cubic units when rounded to the nearest hundredth.

Great job working through