Final answer:
The volume of a sphere is calculated using the formula V = 4/3 (π) (r)^3. This formula represents the actual volume of a sphere and should be used rather than estimating based on dividing a cube into equal squares. The volume is approximately half that of the enclosing cube.
Step-by-step explanation:
Estimating the Volume of a Sphere
When estimating the volume of a sphere based on a cube that encloses it, we can divide the cube into smaller volumes to approach the true volume of the sphere. If we divide the cube into 4 equal squares, we are simplifying the problem into two dimensions, which is less applicable for volume calculation. However, the key information here is in applying the volume formula of a sphere, which is V = 4/3 (π) (r)^3, rather than estimating through subdivisions of a cube. It’s important to note that the volume of a sphere is always less than that of the cube that encloses it. Since the volume of the cube is (2r)^3, the volume of the sphere which has a radius of 'r' is given by the formula above and is approximately half of the cube's volume.
To answer CHECK YOUR UNDERSTANDING 1.5, the volume of a sphere of radius r is given by the formula 4/3 (π) (r)^3, and not the surface area, which is 4 (π) (r)^2. Understanding this concept is fundamental in solving problems related to the volume of a sphere.
For the approximate volume r³ mentioned in the question, considering 'r' as the radius of a sphere and trying to find a plausible dimension for the 7 and factor of (π), may imply inappropriate estimations as they do not conform with the standard formula for the volume of a sphere.