GCSE Arcs Sectors jamiedrfrostmaths com www drfrostmaths com

GCSE : : Arcs & Sectors jamie@drfrostmaths. com www. drfrostmaths. com @Dr. Frost. Maths Objectives: Be able to determine the arc length and area of a sector, and solve problems involving these. (This resource is intended for Higher Tier students only) Last modified: 30 th April 2021

www. drfrostmaths. com Everything is completely free. Why not register? Register now to interactively practise questions on this topic, including past paper questions and extension questions (including UKMT). Teachers: you can create student accounts (or students can register themselves), to set work, monitor progress and even create worksheets. With questions by: Teaching videos with topic tests to check understanding. Questions organised by topic, difficulty and past paper.

Further Resources on this Topic Key Skills allow repetitive practice of randomly generated questions, with short worked example videos and detailed feedback. Teachers can also use these to produce randomly-generated worksheets. Simply type the ‘K___’ into the Dr. Frost. Maths search bar or use the direct link. Key Skill Direct Link K 289: Find the area of the sector of a circle. www. drfrostmaths. com/keyskills. php? ksid=289 K 290: Find the perimeter of a sector of a circle. www. drfrostmaths. com/keyskills. php? ksid=290 K 291: Find the radius of a sector given its area and angle. www. drfrostmaths. com/keyskills. php? ksid=291 K 292: Find the radius of a sector given its arc length and angle. www. drfrostmaths. com/keyskills. php? ksid=292 K 293: Find the angle of a sector given its arc length and radius. www. drfrostmaths. com/keyskills. php? ksid=293 K 294: Find the angle of a sector given its area and radius. www. drfrostmaths. com/keyskills. php? ksid=294 Exam Skills involve broader topic areas and consist of past paper exam questions (as well as user contributions). Teachers can download teaching resources and browse exam questions, and students can practise questions online. Exam Skill Direct Link E 417: Find the area or arc length of more general sectors. https: //www. drfrostmaths. com/resourceexplorer. php? tid=25

www. drfrostmaths. com Everything is completely free. Why not register? Register now to interactively practise questions on this topic, including past paper questions and extension questions (including UKMT). Teachers: you can create student accounts (or students can register themselves), to set work, monitor progress and even create worksheets. With questions by: Dashboard with points, trophies, notifications and student progress. Teaching videos with topic tests to check understanding. Questions organised by topic, difficulty and past paper.

STARTER : : Perimeter/Area of Fractions of Circles ? 1 ? ? 2 10 cm 6 cm 8 cm 3 ? ? Shaded area? ?

Circle Key Definitions ! (Minor) ? Arc It’s a ‘minor’ arc because it’s less than half the circle (Minor)? Sector It’s a ‘minor’ sector because it’s less than half the circle Chord ? (Minor) ? Segment The area on the other side of the chord would be a major segment. Tangent ? Radius ? Diameter ? Circumference ?

Working towards sector area/arc length With the starter activity, you found for example the area of a quarter circle by first calculating the area of a full circle, and then taking a quarter of it/dividing by 4. Identify what fraction (in its simplest form) of the area of each circle you’d use in each case: ? ? ?

Formula for sector area and arc length ! ? ?

Examples ? ? Test Your Understanding: ? ? Fro Tip: Don’t forget the straight edges.

Exercise 1 (on printed worksheet) 1 ?

Exercise 1 2 (on printed worksheet) [AQA GCSE Nov 2012 2 H Q 23] The diagram shows a sector of a circle. Work out the area of the sector. Give your answer to a suitable degree of accuracy. ?

Exercise 1 (on printed worksheet) 3 ?

Exercise 1 4 (on printed worksheet) [Edexcel IGCSE June 2010 -4 H Q 17] The diagram shows a sector of a circle, radius 45 cm, with angle 84°. Calculate the area of the sector. Give your answer correct to 3 significant figures. ?

Exercise 1 (on printed worksheet) 5 ?

Exercise 1 (on printed worksheet) 6 ?

Exercise 1 (on printed worksheet) 7 ?

More Difficult Sector/Arc Problems There a variety of ways that area/sector questions might be more difficult: • Finding the radius or angle (subtended at the centre) of the sector, given the perimeter or arc length or area. • Finding the perimeter given the area of the sector, or vice versa. • Finding the area of a segment (we’ll cover this separately in trig). Use area formula for sector. There’s nothing different here to what you did previously – it’s just that this time the radius is unknown, and we set our area expression to be equal to the known area. Tidy up a bit. We don’t like fractions in equations, so multiply both sides by denominator.

Further Example

Test Your Understanding ?

Exercise 2 1 (on printed worksheet) [Edexcel GCSE March 2013 -2 H Q 19] OAB is a sector of a circle, centre O. The radius of the circle is 15 cm. The angle of the sector is 30°. Calculate the area of sector OAB. Give your answer correct to 3 significant figures. ?

Exercise 2 (on printed worksheet) 2 ?

Exercise 2 (on printed worksheet) 3 ?

Exercise 2 (on printed worksheet) 4 Note: Sine/cosine rule knowledge required for this question. ?

Exercise 2 (on printed worksheet) 5 ?

Exercise 2 (on printed worksheet) 6 ?

Exercise 2 7 (on printed worksheet) [Edexcel GCSE(9 -1) Mock Set 3 Autumn 2017 2 H Q 19] The diagram shows a sector of a circle of radius 9 cm. The sector has a perimeter of 25 cm. Work out the value of x. Give your answer correct to 1 decimal place. ?

Exercise 2 (on printed worksheet) 8 ?

Exercise 2 (on printed worksheet) 9 ?

Exercise 2 10 (on printed worksheet) [Edexcel GCSE Nov 2015 -2 H Q 20] Here are two watch faces, A and B. Both watch faces are circular with radius 2 cm. The materials used to make both watch faces have the same thickness. A is made entirely of plastic. B has a 20° sector of metal and a 340° sector of plastic. The ratio of the cost per cm 2 of the metal to the cost per cm 2 of the plastic is 3 : 2 Work out the ratio of the cost of the materials for A to the cost of the materials for B. Give your answer in its simplest form. You must show all your working. ?

Exercise 2 N (on printed worksheet) [Edexcel GCSE June 2007 -6 H Q 25 b Edited] Here is the net of a cone. The net is a sector of a circle, centre O, and radius 15 cm. Reflex angle AOB = 216° The net makes a cone of slant height 15 cm. Work out the vertical height of the cone ?

BONUS QUESTION [Edexcel IGCSE Jan 2017 -3 H Q 22] The diagram shows a sector OAB of a circle, centre O. Angle AOB = 75° Length of arc AB = 7. 2 cm Calculate the area of the sector. Give your answer correct to 3 significant figures. ?