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GCSE Mathematics Problem Solving Shape and Measure Higher Tier. Helping Hand. 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 .

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Gcse mathematics problem solving shape and measure higher tier

GCSE Mathematics

Problem Solving

Shape and Measure

Higher Tier


Gcse mathematics problem solving shape and measure higher tier

Helping Hand

A company needs a container that is a cuboidand 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.


Gcse mathematics problem solving shape and measure higher tier

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


Gcse mathematics problem solving shape and measure higher tier

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.

78.16 cm = r