TLDR;
This video tutorial explains how to calculate the arc length and sector area of a circle using two different formulas, depending on the information provided in the problem. The first formula is used when there are two angles, two arc lengths, or two sector areas. The second formula is used when there is one angle and the radius of the circle. The video provides step-by-step solutions to example problems, illustrating the application of each formula.
- Two formulas for calculating arc length and sector area are presented.
- The choice of formula depends on the information given in the problem (angles, arc lengths, sector areas, radius).
- Step-by-step examples are provided to illustrate the application of each formula.
Introduction to Arc Length and Sector Area [0:02]
The video introduces the topic of calculating the length of an arc and the area of a sector in a circle. It explains that there are two formulas that can be used, depending on the information provided in the problem. The video encourages viewers to like, subscribe, comment, and share the video.
Formulas for Arc Length and Sector Area [0:40]
The video explains the two formulas used for calculating arc length and sector area. The first formula is applicable when the problem provides two angle sizes, two arc lengths, or two sector areas. The second formula is used when the problem provides one angle size and the radius of the circle.
Example 1: Calculating Sector Area and Arc Length Using the Second Formula [1:39]
This section demonstrates how to calculate the area of a sector (AOB) and the length of an arc (AB) when given one angle and the radius of the circle. To find the area of sector AOB, the formula (Alpha/360) * (Area of Circle) is used, where Alpha is the angle size. Given an angle of 90 degrees and a radius of 14 cm, the area of the sector AOB is calculated as 154 cm². To find the arc length AB, the formula (Alpha/360) * (Circumference of Circle) is used. Using the same angle and radius, the arc length AB is calculated as 22 cm.
Example 2: Calculating Sector Area Using the First Formula [6:58]
This section explains how to calculate the area of a sector (AOB) when given the area of another sector (COD) and the lengths of two arcs (AB and CD). The formula (Area of AOB) / (Area of COD) = (Arc length of AB) / (Arc length of CD) is used. Given the area of sector COD as 48 cm², the arc length AB as 30 cm, and the arc length CD as 12 cm, the area of sector AOB is calculated as 120 cm².