Arc Length And Sector Area Math

Step by step guide to find arc length and sector area of circles.

Arc length and sector area math. Area of a sector πr2 θ 360 π r 2 θ 360 r r is the radius of the circle and θ is the central angle of the sector. Arc of a sector θ 180 πr θ 180 π r. These are the formulas give us the area and arc length that is the length of the arc or curved line for the entire circle. This geometry and trigonometry video tutorial explains how to calculate the arc length of a circle using a formula given the angle in radians the and the len.

Substitute the values in the formula for the area of the sector. Finding area of the sector from arc length. It is full of excellent resources. If you re not familiar with dan meyer s work please visit his wonderful website.

The area of the sector is given by area 1 2 angle aob r 2 1 2 2 r 2 r 2. For a circle with radius 2r and the same central angle what would be the arc length and the sector area. To find the arc of a sector of a circle use this formula. Credit for this original idea goes to dan meyer.

It also separates the area into two segments the major segment and the minor segment. 1 11 ft 315 60 5 ft 2 13 ft 270 61 3 ft 3 16 ft 3 π 2 75 4 ft 4 13 in π 6 6 8 in 5 r 18 cm θ 60 18 8 cm 6 r 16 m θ 75 20 9 m 7 r 9 ft θ 7π 4 49 5 ft 8 r 14 ft θ 19 π 12 69 6 ft. Round your answers to the nearest tenth. Solution to problem 2.

Arc length and sector area date period find the length of each arc. Whenever you want to find area of a sector of a circle a portion of the area you will use the sector area formula. Let nothing fly in the ointment of your skilled practice. Where θ equals the measure of the central angle that intercepts the arc and r equals the length of the radius.

Rearrange the formula of arc length for the radius or central angle. A chord separates the circumference of a circle into two sections the major arc and the minor arc. For a particular circle with radius r the arc length corresponding to a central angle measuring x is l and the area of the related sector is a. Small c 2 pi r c 2πr.

Sector angles area and arc length. To find a sector of a circle use this formula. Calculate the arc length of the sector. His creative approach to making practical problems into interesting learning experiences for students is a treasure for educators.

But sometimes we need to work with just a portion of a circle s revolution or with many revolutions of the circle.