Circles

Question 16: (a) Diagram 16.1 shows a Ferris wheel. The distance between point L and point M is 18 m. Diagram 16.1 Calculate the minimum number of complete spins required to cover the distance of 600 m in a circular motion. (b) Diagram 16.2 shows one large pizza and two small pizzas. Assume all pizzas are circular with a flat … Read more

Question 14: In the Diagram, OKLM is a sector of a circle and OAB is a quadrant of a circle with common centre O. It is given that OA = 8 cm, ∠KOM = 90o and OK : OB = 3 : 2. Using  π= 22 7 , calculate (a) the area, in cm2, of the shaded region, (b) the perimeter, in cm, … Read more

Question 12: Amy will place a ball on top of a pillar in Diagram below. Table below shows the diameters of three balls X, Y and Z. Which ball X, Y or Z, can fit perfectly on the top of the pillar? Show the calculation to support Amy’s choice. Solution: Let the radius of the top of the pillar=r cm. O is the centre of the circle. In Δ OQR, r 2 = ( r−4 … Read more

Question 10: Diagram below shows two quadrants, AOC and EOD with centre O. Sector AOB and sector BOC have the same area. Calculate the area, in cm2, of the coloured region. ( Use π= 22 7 ) Solution: Area of the sector AOB=Area of the sector BOC Therefore, ∠AOB=∠BOC = 90 o ÷2 = 45 o Area of the coloured region = 45 o 360 o × 22 7 × 16 … Read more

Question 7: In diagram below, ABC is a semicircle with centre O. Calculate the area, in cm2 , of the shaded region. ( Use π= 22 7 ) Solution: ∠ACB= 90 o AB= 6 2 + 8 2 = 100 =10 cm Radius=10÷2    =5 cm The shaded region =( 1 2 × 22 7 ×5×5 )−( 1 2 ×6×8 ) … Read more

Question 4: Diagram below shows two sectors. ABCD is a quadrant and BED is an arc of a circle with centre C. Calculate the area of the shaded region, in cm2. ( Use π= 22 7 ) Solution: The area of sector CBED = 60 o 360 o ×π r 2 = 60 o 360 o × 22 7 × … Read more

5.2.1 Circles, PT3 Focus Practice Question 1: Diagram below shows a circle with centre O.   The radius of the circle is 35 cm. Calculate the length, in cm, of the major arc AB. ( Use π= 22 7 )   Solution: Angle of the major arc AB = 360o – 144o= 216o Length of major … Read more

5.1.2 Circumference of a Circle    circumference=πd,      where d=diameter                            =2πr,     where r=radius                                    π(pi)= 22 7      or   3.142 Example: Calculate the circumference of a circle with a diameter of 14 cm. ( π= 22 7 ) Solution: Circumference=π× Diameter                       = 22 7 ×14                       =44 cm 5.1.3 Arc of a Circle The length of an arc of a circle is proportional to the angle … Read more

5.1a Circles   5.1.1 Parts of a Circle 1. A circle is set of points in a plane equidistant from a fixed point. 2. Parts of a circle: (a)    The centre, O, of a circle is a fixed point which is equidistant from all points on the circle. (b)   A sector is the region enclosed by two … Read more