N 4 Revision Area of a Circle EF

N 4 Revision Area of a Circle E&F

Area of a Circle Radius D = 2 x R R=D÷ 2 Diameter

Area of a Circle Exercise 1 State the radius of each circle: 6 cm 10 cm R = 6 cm R = 10 ÷ 2 R = 5 cm

Area of a Circle Exercise 1 a) e) R = 8 cm 4 cm R = 5 m 5 m State the radius of each circle: b) f) R = 3 cm R =10. 4 cm 5. 2 cm c) g) R = 27 cm 54 m R = 4. 2 cm d) R = 6 cm 12 cm h) R = 9. 6 m 4. 8 m

Area of a Circle Examples Find the area of each circle: c) b) a) R=8 8 cm Area = π x r 2 = 3. 14 x 8 = 200. 96 cm² R = 3. 2 m R = 10 Area = π x r 2 = 3. 14 x 3. 2 = 140 m² 10 mm Area = π x r 2 = 3. 14 x 10 = 314 mm² Must show these 3 lines of working!

Exercise 2 Find the area of the each circle to 2 dp: 50. 24 cm 2 13. 85 m 2 452. 16 cm 2 72. 35 mm 2 2826 cm 2 615. 44 m 2 4 cm 4. 8 mm 2. 1 m 30 cm 12 cm 14 m

Area of a Circle Examples a) R=3 Must show at least 3 lines of working! Find the area of each circle: c) b) 6 cm Area = π x r 2 = 3. 14 x 3 = 28. 26 cm² R = 2. 1 4. 2 m Area = π x r 2 = 3. 14 x 2. 1 = 13. 8474 = 13. 85 m² R = 12. 5 25 mm Area = π x r 2 = 3. 14 x 12. 5 = 490. 625 = 490. 63 mm²

Exercise 3 Find the area of the each circle to 2 dp: 12. 56 cm 2 379. 94 m 2 36. 30 mm 2 706. 50 cm 2 4 cm 6. 8 mm 22 m 30 cm 2 132. 67 mm 13 mm 2 1384. 74 cm 42 mm

Area of a Semi-Circle Must show at least 3 lines of working! Examples Find the area of each semi-circle: c) b) a) 6 cm R=6 A = (π x r 2) ÷ 2 = (3. 14 x 6 x 6) ÷ 2 = 113. 04 ÷ 2 = 56. 52 cm² R=7 7 mm A = π x r 2 = (3. 14 x 7 x 7) ÷ 2 = 153. 86 ÷ 2 = 76. 93 mm² R = 11 11 m A = π x r 2 = (3. 14 x 11) ÷ 2 = 379. 94 ÷ 2 = 189. 97 m²

Exercise 4 Find the area of the each semi-circle to 2 dp: 6. 28 cm 2 29. 03 m 2 2 cm 4. 3 m 237. 53 m 2 39. 25 cm 2 12. 3 m 5 cm 127. 17 mm 2 9 mm 560. 82 mm 2 18. 9 m

Area of a Semi-Circle Must show at least 3 lines of working! Examples a) 16 cm Find the area of each semi-circle: c) b) R=8 A = (π x 200 m R = 100 r 2) ÷ 2 = (3. 14 x 8 x 8) ÷ 2 = 200. 96 ÷ 2 = 100. 48 cm² A = (π x r 2) ÷ 2 = (3. 14 x 100) ÷ 2 = 31400 ÷ 2 = 15700 m² 70 mm R = 35 A = (π x r 2) ÷ 2 = (3. 14 x 35) ÷ 2 = 3846. 5 ÷ 2 = 1923. 25 mm²

Exercise 5 Find the area of the each semi-circle to 2 dp: 2639. 17 cm 2 82 cm 157 cm 2 20 cm 830. 53 mm 2 46 mm 2149. 33 m 2 74 m 3925 cm 2 100 cm 401. 92 cm 2 32 cm

Area of a Quarter Circle Must show at least 3 lines of working! Examples Find the area of each quarter circle to 1 dp: c) b) a) R=3 9 mm 3 cm R=9 A = (π x r 2) ÷ 4 = (3. 14 x 9 x 9) ÷ 4 = (3. 14 x 3 x 3) ÷ 4 = 254. 34 ÷ 4 = 113. 04 ÷ 4 = 63. 585 mm² = 7. 065 cm² = 63. 6 mm² = 7. 1 cm² R=1 1 m A = (π x r 2) ÷ 4 = (3. 14 x 1 x 1) ÷ 4 = 3. 14 ÷ 4 = 0. 785 m² = 0. 8 m²

Exercise 6 Find the area of the each quarter circle to 1 dp: 4 cm 10 m 12. 56 cm 2 78. 5 m 2 44 m 1519. 8 m 2 32 cm 803. 8 cm 2 19 mm 283. 4 mm 2 16 mm 201. 0 mm 2

? Area of Composite Shapes Example Find the area of : Area A = l x b = 20 x 8 = 160 cm² 20 cm A 8 cm B (R = 4) Area B = (π x r 2) ÷ 2 = (3. 14 x 4) ÷ 2 = 50. 24 ÷ 2 = 25. 12 cm 2 Total Area = 160 + 25. 12 =210. 24 cm²

? Area of Composite Shapes Example Area A = l x b = 15 x 17 A 15 cm Find the green shaded area to 1 dp B 3 cm 17 cm = 255 cm² Area B = π x r 2 = 3. 14 x 1. 5 = 7. 065 cm² Green shaded Area = 450 - 7. 065 = 442. 935 = 442. 9 cm²

Exercise 7 1) Find the total area : Area A = 48 m 2 B Area A = 14. 13 m 2 A 8 m Total Area= 62. 13 m 2 6 m Click here to see full solution

Exercise 7 2) Find the total area : 12 cm 30 cm 12 cm Area Triangle = 180 cm 2 Area Quarter circle = 113. 04 cm 2 Total Area= 293. 04 cm 2 Click here to see full solution

Exercise 7 3) Find the yellow shaded area : A semi-circle has been cut from the original rectangle). Area Rectangle = 2800 cm 2 70 cm 44 cm Area semi-circle = 759. 88 cm 2 Total Area= 2040. 12 cm 2 40 cm Click here to see full solution

Exercise 8 Find the area of the following shapes: 11 cm 6 cm 94. 26 cm 2 104. 13 cm 2 15 cm Find the shaded area : 14 cm 152. 52 cm 2 2067. 34 cm 2 8 cm 12 cm 13 cm 55 cm 40 cm

Exercise 7 Find the total area : A A= lxb A= 8 x 6 A = 48 m 2 B D = 6 m R = 3 m A = x r 2 A = 3. 14 x 3 x 3 A = 28. 26 m 2 B A 6 m TOTAL AREA = 8 m Semi-circle = 14. 13 m 14. 13 2 48 + 14. 13 = 62. 13 m 2 Bac. K

Exercise 7 2) Find the total area : A 12 cm B 30 cm A A= ½xbxh A = ½ x 30 x 12 A = 180 cm 2 TOTAL AREA= 12 cm r = 12 cm A= x r 2 A = 3. 14 x 122 A = 452. 16 cm 2 ¼-circle = 113. 04 cm 2 B 180 + 113. 04 = 293. 04 cm 2 Back

Exercise 7 3) Find the yellow shaded area : A semi-circle has been cut from the original rectangle). Rectangle: A= lxb A = 70 x 40 A = 2800 cm 2 70 cm 44 cm Whole Circle D = 44 cm r = 22 cm A= x r 2 A = 3. 14 x 222 A = 1519. 76 cm 2 40 cm Area of shape = Semi-circle = 759. 88 cm 2 2800 - 759. 88 = 2040. 12 cm 2 Back