Mathematics Higher Level Robert Joinson

©Sumbooks 2002Higher Level50. Area and Perimeter1. Calculate the area of the trapezium on the right.2. Calculate the area of the shaded part of the ring below.6cm8cm9cm dia.9cm6cm dia.3. Calculate the area and arc length of the following sectors where r is the radius of the circleand θ is the angle at the centre of the circle.a) r = 6cm b) r = 12cm c) r = 16.5cm d) r = 16.75cmθ = 30°θ = 140°θ = 200°θ = 195°4. The shaded part of the diagram shows a flower garden inthe shape of an arc. It has an inside radius of 4 metres andan outside radius of 9 metres. a) Calculate the area of thegarden. b) If it is completely surrounded by an edging strip,calculate its length.5. A conical lamp shade is to be made from the piece of fabricshown in the diagram. a) Calculate its area. b) If a fringe issewn onto it’s bottom edge, what length will it be?25cm170°20cm4m75°9m6. A water tank is in the form of a cylinder of 4 metres diameter and 4metres high, open at the top. It is to be made from sheet steel andpainted with three coats of paint, both inside and outside. Calculatea) the total area of steel needed and b) the number of tins of paintneeded if one tin is sufficient to cover 28m 27. The ceiling of a church is in the shape of a hemisphere. If its radiusis 8 metres, calculate its surface area.8. The diameter of the earth is approximately 12734 kilometres.Calculate its surface area.4m4m