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
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
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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