Perimeter, Area and Volume: Age 14-16
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This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
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Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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Where should runners start the 200m race so that they have all run the same distance by the finish?
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Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
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An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
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Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
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Various solids are lowered into a beaker of water. How does the water level rise in each case?
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In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
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A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?
