Question The diagram shows a metal plate OABCDEF consisting of 3 sectors, each with centre O. The radius of sector COD is 2r and angle COD is radians. The radius of each of the sectors BOA and FOE is r, and AOED and CBOF are straight lines. i. Show that the area of the metal plate is . ii. Show that […]
Question The diagram shows a metal plate OABC, consisting of a right-angled triangle OAB and a sector OBC of a circle with centre O. Angle AOB = 0.6 radians, OA = 6 cm and OA is perpendicular to OC. i. Show that the length of OB is 7.270 cm, correct to 3 decimal places. ii. Find the perimeter of […]
Question The diagram shows a circle with centre A and radius r. Diameters CAD and BAE are perpendicular to each other. A larger circle has centre B and passes through C and D. i. Show that the radius of the larger circle is . ii. Find the area of the shaded region in terms of . Solution i. […]
Question In the diagram, OAB is a sector of a circle with centre O and radius r. The point C on OB is such that angle ACO is a right angle. Angle AOB is radians and is such that AC divides the sector into two regions of equal area. i. Show that It is given […]
Question In the diagram, AYB is a semicircle with AB as diameter and OAXB is a sector of a circle with centre O and radius r. Angle AOB = 2 radians. Find an expression, in terms of r and , for the area of the shaded region. Solution It is evident from the diagram that; First we calculate area […]
Question A piece of wire of length 24 cm is bent to form the perimeter of a sector of a circle of radius r cm. i. Show that the area of the sector, A cm2, is given by . ii. Express A in the form , where a and b are constants. iii. Given that r can vary, state […]