Mathematics Higher Level Robert Joinson

©Sumbooks 2002Higher Level51. Volume1. Calculate the volume of a 12cm square based pyramid with a height of 20cm.2. Calculate the height of a 4cm square based pyramid whose volume is 40cm 33. A rolling pin is in the shape of a cylinder with hemispherical ends. Its total length is 40cmand its diameter is 5cm. Calculate a) its volume and b) its weight if 1cm 3 of wood weighs0.75 grammes.4. A marble paperweight is in the shape of a hemisphere of radius 4cm. Calculate its volume.A supplier packs them into boxes of 50. Calculate their weight, correct to the 0.1kg, if 1cm 3of marble weighs 2.7 grammes.5. A metal sphere of diameter 10cm is lowered into a cylindrical jar of 16cm height and 12cmdiameter which contains water to a depth of 10cm. How far up the side of the jar will thewater rise?6. The diagram shows a swimming pool. It22mmeasures 22 metres long by 10 metres wide.10mIt is 1 metre deep at the shallow end and 2 1mmetres deep at the other end. Calculate the2mamount of water it will hold, in litres.7. A bucket is made by cutting a cone into two parts, as shown in thediagram. If the rim of the bucket measures 30cm diameter, calculateBucketthe amount of water it will hold, correct to the nearest litre.40cm8. A piece of metal, in the shape of a square based pyramid of height10cm and base sides of 5cm, is melted down and re-cast into spheres 40cmof diameter 3mm. How many spheres can be made?9. Plastic plant pots are made in the shape of inverted 5cmtruncated pyramids. The top is a square of 5cm sides, thebottom a square of 3cm sides and its height is 6cm.a) Calculate its volume b) How many can be filled froma bag containing 2 litres of compost.?10. Tennis balls of 6cm diameter are packed into cubic boxeswhich hold 27 balls. Calculate a) the volume of the boxb) the percentage of the box filled by the tennis balls.11. A measuring cylinder with a base diameter of 3.8cm contains water. 500spheres of diameter 5.3mm are dropped into it and are completely coveredby water. Calculate the height by which the water rises.12. A hollow metal sphere has an outside diameter of 10cm and is 1cm thick.Calculate the volume of the metal.13. The diagram shows a wine glass. The bowl is in the shape of a hemispherewith part of a cone on top of it. The diameter of the hemisphere is 7cm andthe height of the cone is 14cm. The diameter of the rim of the glass is 6cmand is 2cm above the hemisphere. Calculate the amount of wine the glasswill hold, correct to the nearest millilitre.3cm6cm6cm14cm