Geometry Formulas and Calculations

This page provides a comprehensive overview of geometric formulas and calculations related to circles, sectors, and cylinders. It serves as a quick reference guide for students studying these topics.

The page begins with the fundamental formulas for area of a circle and circumference.

Definition: The area of a circle is calculated using the formula A = πr², where r is the radius.

Definition: The circumference of a circle is calculated using the formula C = πd, where d is the diameter.

The document then moves on to more advanced concepts such as arc length and sector area.

Vocabulary: Arc length is defined as the distance between two points along a section of a circle.

Example: An example calculation is provided for arc length, where the angle of the sector is 145° out of 360°, and the circumference is 25.12 units. The arc length is calculated as $145/360$ × 25.12 = 10.09 units.

The page also covers sector area calculations.

Highlight: The sector area is calculated as a fraction of the circle's total area, based on the angle of the sector.

Example: A worked example shows how to find the area of a sector with an angle of 145° in a circle with a total area of 50.24 square units. The calculation is $145/360$ × 50.24 = 20.22 square units.

The final section of the page focuses on cylinders, providing formulas for surface area and volume.

Definition: The surface area of a cylinder is given by the formula SA = 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder.

Example: A detailed example calculates the surface area of a cylinder with a radius of 4 units and a height of 10 units, resulting in a total surface area of 351.68 square units.

Definition: The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height.

Example: The volume of the same cylinder is calculated as 502.4 cubic units.

This comprehensive guide provides students with a solid foundation for understanding and applying geometric concepts related to circles, sectors, and cylinders.