5 Problem-solving a Mark a dot on the edge of a 2p coin and align it with the zero mark on a ruler. b Roll the coin along the ruler to find the circumference of the coin. c Use the circumference to estimate the diameter of the coin. d Repeat parts b and c, but this time roll the coin 4 times. Discussion Which method should give you a more accurate answer for the diameter of the coin? Explain your answer. e Measure the diameter of the coin. Which method was the most accurate? Q6 hint 6 Real A trundle wheel clicks every time it travels 1 m. Work out the diameter of the trundle wheel in centimetres to 1 decimal place. Use C = pd What is the circumference of the trundle wheel? 7 Real / Modelling A penny-farthing bicycle has a large front wheel and a small back wheel. The radius of the front wheel is 74 cm. a i How far does the wheel travel in one revolution? Give your answer in metres to 1 decimal place. ii How many revolutions will it go through when travelling 100 m? Over the same distance, the back wheel rotates 108 times. b i What is the circumference of the back wheel? Round your answer to 1 decimal place. ii What is the radius of the back wheel? Round your answer to 1 decimal place. 8 The diagram shows a square-based pyramid. a Write the length of the distance x. b Use Pythagoras’ theorem to calculate <, the slant height of the pyramid. c Calculate the area of one triangular face of the pyramid. d Calculate the area of the base of the pyramid. e Calculate the surface area of the pyramid. f Calculate the volume of the pyramid. 9 Modelling The diagram shows a car wheel. a Work out the circumference of the wheel to the nearest cm. On a journey to work and back, the wheel rotates 50 000 times. b What is the total length of the journey? Give your answer in kilometres to 1 decimal place. Key point Volume of a pyramid = 13 × area of base × height 7 cm ᐉ x 6 cm 6 cm 47.5 cm Q9b hint 1 m = 100 cm 1 km = 1000 m Unit 3 2D shapes and 3D solids 70