Find the length of an arc on a semicircle and quarter circle and the perimeter of a semicircle and quarter circle.

What is the arc length of the semi circle in terms of π ?

What is the arc length of the quarter circle to 3 significant figures?

What is the arc length of the semicircle to 3 significant figures?

Find the length of an arc on a semicircle and quarter circle and the perimeter of a semicircle and quarter circle

﻿Hello, my name is Miss Parnham. In this lesson, we're going to learn, how to find the length of an arc, and the perimeter of a sector. Lets work out the perimeter of this sector. We start by working out the circumference of a circle, with the same radius as this sector, which is pi multiplied by two multiplied by the radius, to give us 30 pi or 94.2 metres to three significant figures. But this sector has an angle of 240 degrees, which is two thirds of 360 degrees. So the arc length is two thirds of the circumference. So we must take this 30 pi divided by three, and multiply it by two to get 20 pi, which to three significant figures is 62.8 metres. So the perimeter we need to add two radii onto the 20 pi to give us our final answer. This is either 20 pi plus 30 metres or 92.8 metres, to three significant figures. Here's some questions for you to try, pause the video, to complete the task, and restart the video when you're finished. Here are the answers, hopefully question one helped you to solve question two, by dividing 12 pi by three, for the arc length. When finding the perimeter, is then important to remember, to add two radii onto this arc length. And that's why the answer is four pi plus 24. Here is some further questions for you to try. Pause the video, to complete the task, and restart the video when you're finished. Here are the answers. In part C the angle outside the sector is given. So you need to remember to subtract 220 from 360, to get the angle inside the sector as 240 degrees. Let's find the perimeter of this sector, and to do that, we need the arc length. And to find that, we need to know the circumference of a circle with the exactly the same radius of this sector. So that's pi multiplied by two multiplied by 12.6, which is 25.2 pi or 79.2 centimetres, to three significant figures. This sector has an angle of 234 degrees. So in order to work out what fraction of the circumference, the arc length is, we divide 234 by 360, because it's the same fraction that the angle is of the 360 degrees inside circle. So our arc length is 79.2 multiplied by 234, over 360. This gives us 51.5 centimetres to three significant figures. Remember we've written a rounded answer down, but we are working with a full answer in our calculator because to this arc length, we need to add two radii of 12.6 each, to get the final perimeter of this sector. So to three significant figures, this is 76.7 centimetres. Here's some questions for you to try, pause the video to complete the task, and restart the video when you're finished. Here are the answers. These questions show that whether we have an acute, an obtuse or reflex angle inside a sector, we use exactly the same method to first find the arc length, and then the perimeter. Here's a further question for you to try, pause the video to complete the task, and restart the video when you're finished. Here are the answers. In this question you needed to find two arc lengths of a sector with a seven centimetre radius, and one with a 10 centimetre radius. The 10 centimetres is coming from adding the seven centimetres and the three centimetres together. In addition, you need to add two straight pieces, both equal in three centimetres and adding that all together would give you the final perimeter. That's all for this lesson. Thank you for watching.

Find the length of an arc and the perimeter of a sector

What is the arc length of the sector to 3 significant figures?

What is the perimeter of the sector to 3 significant figures?

In this lesson, we will find the length of an arc and the perimeter of a semicircle

Lesson overview:Find the length of an arc and the perimeter of a sector

Core Content

Parts of circles 2 (Arcs and Sectors):