Sphere and Cylinder Formulas and Problems

This page introduces important formulas for spheres and provides example problems applying those formulas.

The fundamental formulas for spheres are presented:

Definition: The pole kuli (surface area of a sphere) is given by the formula P = 4πr², where r is the radius.

Definition: The objętość kuli (volume of a sphere) is given by the formula V = 4/3πr³.

Two sample problems are then worked through:

Problem 1 involves finding the radius of a sphere given its volume of 288π cubic units.

Example: Using the volume formula V = 4/3πr³, we can set up the equation: 288π = 4/3πr³ Simplifying and solving for r gives a radius of 6 units.

Problem 2 compares the volumes of a sphere and cylinder:

Example: A sphere with radius 6 and a cylinder with height 4.5 have equal volumes. The problem asks to find the diameter of the cylinder's base. Using the volume formulas for both shapes and setting them equal allows solving for the cylinder's radius, which is found to be 8 units.

Highlight: The diameter of the cylinder's base is therefore 16 units (2r).

These examples demonstrate practical applications of the wzór na objętość kuli (sphere volume formula) and how to compare volumes of different 3D shapes.