Question

the volume of a sphere is derived by comparing the sphere to a that surrounds it. in the formula ( v=\frac{4}{3}pi r^{3} ), the variable ( r ) represents the of the sphere. if the diameter of a sphere is given, you can find the radius by dividing the diameter by. the volume of a sphere is measured in units.

Explanation:

• For the first blank: The volume of a sphere is derived by comparing it to a cylinder (a well - known geometric relationship in volume derivation).
• For the second blank: In the formula \(V=\frac{4}{3}\pi r^{3}\), \(r\) is the radius (a standard variable definition in the sphere volume formula).
• For the third blank: Since \(d = 2r\) (diameter - radius relationship), if \(d\) is given, \(r=\frac{d}{2}\).
• For the fourth blank: Volume is measured in cubic units (a fundamental unit property for three - dimensional measures).

Answer:

1. cylinder
2. radius
3. \(2\)
4. cubic