Starter quiz
The perimeter of this shape is ______ cm.- '68' ✓
- A circle has a diameter of 38 cm. Which of these are correct for the circumference of this circle?
- The circumference is cm.
- The circumference is cm. ✓
- The circumference is cm.
- The circumference is 119 cm (nearest integer). ✓
- The circumference is 238 cm (nearest integer).
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- A circle has a radius of 600 cm. Which of these are correct for the area of this circle?
- The area is 600 cm².
- The area is 600² cm.
- The area is 600² cm². ✓
- The area is 360 000 cm.
- The area is 360 000 cm². ✓
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The perimeter of shape B is ______ cm bigger than the perimeter of shape A.- '7.12' ✓
The perimeter of this shape is ______ metres.- '2.4 ' ✓
Use Pythagoras’ theorem to help you complete this statement. The perimeter of the triangle is ______ cm correct to 1 d.p.- '37.6' ✓
Exit quiz
The sector comes from this circle. The arc length of this sector is ______ cm.- '80' ✓
The sector comes from this circle. The perimeter of the sector is ______ cm.- '50' ✓
- The radius of a circle is 10 cm. The circumference of the circle is 20 cm. A semicircle is taken from this circle. Which of these statements are correct about this semicircle?
- The arc length of the semicircle is 5 cm.
- The arc length of the semicircle is 10 cm. ✓
- The arc length of the semicircle is 20 cm.
- The perimeter of the semicircle is (10 + 10) cm.
- The perimeter of the semicircle is (10 + 20) cm. ✓
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Which of these statements are correct about the arc length of this sector?- The arc length is .
- The arc length is . ✓
- The arc length is . ✓
- The arc length is 41.8 cm (1 d.p.)
- The arc length is 42 cm (nearest integer). ✓
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The perimeter of this sector is ______ cm (to the nearest centimetre).- '889' ✓
The diagram shows a sector. The chord between the endpoints of its radii is 350 cm. The arc length of the sector is ______ cm (to the nearest centimetre).- '389' ✓
Worksheet
Presentation
Video
Lesson Details
Key learning points
- Using fractions, you can calculate part of the circumference.
- This gives the length of the curved section of a sector.
- To find the perimeter, you will need to add the radius twice.
- An exact answer may be given in terms of π
Common misconception
"When finding the perimeter of a sector, I need to multiply the radius by a fraction of a full circle, just like I did with the circumference to find the arc length."
Reminder that only part (the arc length) of the formula for perimeter of a sector varies with the angle. A desmos or geogebra model can help to show this.
Keywords
Arc - An arc is part of a curve. An arc of a circle is part of the circle’s circumference.
Sector - A sector is the region formed between two radii and their connecting arc.
Chord - A chord is any line segment joining two points on the circumference of a circle.
Radius - The radius is any line segment that joins the centre of a circle to any point on its circumference.
Circumference - The circumference of a circle is the perimeter of the circle.