Programme 6 Area of Circles and Composite Shapes Worksheet 1: Programme Questions

Transcription

1 Worksheet 1: Programme Questions 1. The large pizza is a 12 inch one. What is the diameter of the smaller size pizza? 2. What formula gives the area of a circle? 3. Whose pizza was better value, Katie s or Jamie s? 4. What is the diameter of each disc cut from the aluminium? 5. How many cans are manufactured at this factory each day? 6. In Tick or Trash, what value of π does the question give? 7. What units are used for the area of the path? 8. We see a composite shape made up of 2 quarter circles and one other shape. What is it? 9. What shape are the bends on the athletics track? 10. The presenters measure the length of the straight as 85m. What is the distance between the straights that they also measured? Channel Four Television Corporation 2002 page 1 of 6

2 Worksheet 2: Tick or Trash Here are some questions and answers (by Students A and B) on areas of circles and composite shapes. Decide which answers to Tick (correct) and which to Trash (incorrect). Give reasons. Question 1 This diagram shows the plan of a floor. Work out the area of the floor. 12m 11m 5m Student B Answer 4m Student A Answer Student B adds the dotted line shown on below and the length 8m to the side shown. Area = (5 x 8) + (4 x 11) Area = (12 x 5) + (11 x 4) = = = 84m 2 12m = 104m 2 11m 8m 5m 4m Question 2 The radius of a circle is 5.1m. Work out the area of the circle. State the units of your answer. 5.1m Student A Answer A = πr 2 π = 3.14 r = 5.1 = 3.14 x 5.1 x 5.1 = = 81.7m 2 (3sf) Student B Answer A = πr 2 = π x = = 257cm 2 Channel Four Television Corporation 2002 page 2 of 6 page 2 of 4

3 Question 1 National curriculum reference: N3d Date: June 1996 Paper: 2 Some oil is spilt. The spilt oil is in the shape of a circle. The circle has a diameter of 12 centimetres. (a) Work out the circumference, in centimeters, of the spilt oil. Give your answer correct to 1 decimal place. The diameter of the spilt oil increases by 30% (b) Work out the new diameter, in centimetres, of the spilt oil. [5] Question 2 National curriculum reference: N4d Date: June 1996 Paper: 4 Jomo is going to design a circular roundabout. The roundabout will have a circumference of 7 metres. Jomo is given three estimates for the length of the diameter of the roundabout. The estimates are: metres 2 metres 2.23 metres (a) Give a reason why 2.23 metres is the most reasonable estimate to use. (b) Explain why metres and 2 metres are not appropriate to use. [3] Question 3 National curriculum reference: S4d Date: June 1997 Paper: 1 (a) Work out the perimeter of the whole shape ABCD. In part b you must write down the units with your answer. (b) Work out the area of i) the square EBCD, ii) the triangle ABE [7] Channel Four Television Corporation 2002 page 3 of 6

4 Question 4 National curriculum reference: S4d Date: June 1996 Paper: 1 1cm represents 10km. An earthquake has its centre at the centre of the circle shown in the scale drawing and affects everywhere inside the circle. (a) Find the actual radius, in kilometres, of the circle affected by the earthquake. (b) Calculate the area affected by the earthquake. Give your answer in km 2 correct to the nearest whole number. [6] Question 5 National curriculum reference: S4d Date: November 1997 Paper: 3 The diagram shows a circle of diameter 70cm inside a square of side 70cm. Work out the area of the shaded part of the diagram. Give your answer correct to 3 significant figures. [6] Question 6 National curriculum reference: S4d Date: June 1996 Paper: 1 Here is a side view of a swimming pool. ABCD is a horizontal straight line. AH, BG, CF and DE are vertical lines. (a) Write down the mathematical name for the quadrilateral BCFG. (b) Work out the area of quadrilateral BCFG. [5] Channel Four Television Corporation 2002 page 4 of 6

5 Question 7 National curriculum reference: S4d Date: June 1995 Paper: 1 Mary has a circular dining table with a radius of 0.65m. (a) Work out the area of the top of the table. Give your answer to 3 significant figures. The perimeter of the circular tablecloth is 5m. (b) Work out the diameter of the tablecloth. [6] Question 8 National curriculum reference: S4d Date: June 1998 Paper: 3 Shape A Shape B Diagrams NOT (a) Work out the area of Shape A. (b) i) Work out the perimeter of the semicircle, Shape B. ii) Work out the area of the semicircle, Shape B, in cm 2. (2 marks) (5 marks) [7] Question 9 National curriculum reference: S4d Date: June 1999 Paper: 4 This diagram shows the floor plan of a room. Work out the area of the floor. Give the units with your answer. [4] Channel Four Television Corporation 2002 page 5 of 6

6 Question 10 National curriculum reference: S4d Date: June 1999 Paper: 3 The diagram shows a right-angled triangle ABC and a circle. A, B and C are points on the circumference of the circle. AC is the diameter of the circle. The radius of the circle is 10cm. AB = 16cm and BC = 12cm. Work out the area of the shaded part of the circle. Give your answer correct to the nearest cm 2. [6] Total = 55 Channel Four Television Corporation 2002 page 6 of 6