GCSE Mathematics Problem Solving Shape and Measure Higher Tier

A company needs a container that is a cuboid and has a base of area 1m², to hold 6000 litres of water. a) Find the height of the cuboid. b) The company also need a container that is sphere and that will hold a third of the water of the cuboid. What is the radius of the sphere? Find the volume of the water. (a) Use the formula for the volume of the container to find the containers height. (b) Use the formula for the volume of a sphere to find the radius of the sphere. Helping Hand

Answer (a)Volume of the water 1 litre = 1 000cm³ 6,000 litre = 6,000,000 cm³ Area of the base 1m = 100cm 1m²= 100cm x 100cm 1m² = 10,000cm² Volume = Area of the base x height 6,000,000 = 10,000 x height 6,000,000 ÷ 10,000 = height 600cm = height 100 cm = 1 m Height = 6m

Answer b) Volume of the sphere 6,000 ÷ 3 = 2,000 litre 2,000 litre = 2,000,000 cm³ Change the subject of the formula to find r cm = r