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MADELINE CONROY
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This document covers key concepts in geometry, focusing on circles, sectors, and cylinders. It includes formulas for area, circumference, arc length, and volume, along with practical examples and calculations.
5/31/2023
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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.
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MADELINE CONROY
@madeline_22
·
8 Followers
Follow
This document covers key concepts in geometry, focusing on circles, sectors, and cylinders. It includes formulas for area, circumference, arc length, and volume, along with practical examples and calculations.
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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.
Average App Rating
Students use Knowunity
In Education App Charts in 12 Countries
Students uploaded study notes
iOS User
Stefan S, iOS User
SuSSan, iOS User
