Question

The model of a building is constructed with scale factor 1: 30. (4) (i) if the height of the model is 80 cm, find the actual height of the building in metres. (ii)if the actual volume of the tank on the top of the building is 27m3 , find the volume of the tank on the top of the model. Also, express your answer in litres

Answer 1

Scale Factor = 1 : 30

Question (i):

Convert cm to m (actual):

1 cm = 30 cm

1 cm = 0.3 m

Find 80 cm:

80 cm = 0.3 x 80 = 24 m

Answer: The height of the building is 24 m

Question (ii):

Convert cm to m (actual)

1 cm = 30 cm

1 cm = 0.3 m

Find 1 m (actual):

0,3 m = 1 cm

1 m  = 1 ÷ 0.3 = 10/3 cm

FInd 1 m³:

1m = 10/3 cm

(1m)³ = (10/3 cm)³

1 m³ = 1000/27 cm²

Find 27 m³:

27 m³ = 1000/27 x 27 = 1000 cm³

Convert 1000 cm³ to litres:

1 cm³ = 0.001 litres

1000 cm³ = 0.001 x 1000

1000 cm³ = 1 litres

Answer: The volume is 1 litres

Answer 2

Scale Factor = 1 : 30

Question (i):

Convert cm to m (actual):

1 cm = 30 cm

1 cm = 0.3 m

Find 80 cm:

80 cm = 0.3 x 80 = 24 m

Answer: The height of the building is 24 m

Question (ii):

Convert cm to m (actual)

1 cm = 30 cm

1 cm = 0.3 m

Find 1 m (actual):

0,3 m = 1 cm

1 m  = 1 ÷ 0.3 = 10/3 cm

FInd 1 m³:

1m = 10/3 cm

(1m)³ = (10/3 cm)³

1 m³ = 1000/27 cm²

Find 27 m³:

27 m³ = 1000/27 x 27 = 1000 cm³

Convert 1000 cm³ to litres:

1 cm³ = 0.001 litres

1000 cm³ = 0.001 x 1000

1000 cm³ = 1 litres

Answer: The volume is 1 litres

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