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Unit Conversion, SM-Bank 023

  1. By considering the dimensions of a square with an area of 1 square kilometre, complete the unit conversion equation below:

1 km² = ________ m  ×  ________ m = ______________ km²   (1 mark)

  1. The Barangaroo precinct in Sydney has a total floor space of 681 000 square metres.
  2. Find the area of this floor space in square kilometres.  (1 mark)
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Unit Conversion, SM-Bank 022

  1. By considering the dimensions of a square with an area of 1 square kilometre, complete the unit conversion equation below:

1 km² = _______ m  ×  _______ m = ____________ km²   (1 mark)

  1. A rural property is in the shape of a rectangle with sides of length 1.20 kilometres and 2.36 kilometres.
  2. Find the area of the property in square kilometres and using the conversion equation, express the area in square metres.  (2 marks)
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Unit Conversion, SM-Bank 021

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A circular poster has an area of 0.09 square metres.
  2. Express this area in square centimetres, giving your answer in exact form.  (1 mark)
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Unit Conversion, SM-Bank 020

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A circular stage has an area of 265 000 square centimetres.
  2. Express this area in square metres.  (1 mark)
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Unit Conversion, SM-Bank 019

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A rectangular serviette has an area of 0.075 square metres.
  2. Express this area in square centimetres.  (1 mark)
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Unit Conversion, SM-Bank 018

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A doubles tennis court has an area of 260 square metres.
  2. Express this area in square centimetres.  (1 mark)
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Unit Conversion, SM-Bank 017

  1. By considering the dimensions of a square with an area of 1 square metre, complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A circular elevator has a diameter of 1.6 metres.
  2. Find the area of the elevator's floor in square metres and using the conversion equation, express the area to the nearest square centimetre.  (2 marks)
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Unit Conversion, SM-Bank 016

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = _______ cm²   (1 mark)

  1. A circular playground has an area of 2000 square metres.
  2. Using the conversion equation, or otherwise, express the area in square centimetres.  (1 mark)
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Unit Conversion, SM-Bank 015

The square below has an area of 1 square centimetre.
 

  1. Complete the unit conversion equation below:

1 cm² = _____ mm  ×  _____ mm = _______ mm²   (1 mark)

  1. A rectangle has an area of 1100 square millimetres.
  2. Using the conversion equation, or otherwise, express the area of the circle in square centimetres.  (1 mark)
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Unit Conversion, SM-Bank 014

  1. By considering the dimensions of a square with an area of 1 square centimetre, complete the unit conversion equation below:

1 cm² = _____ mm  ×  _____ mm = _______ mm²   (1 mark)

  1. A circle has an area of 950 square centimetres.
  2. Using the conversion equation, or otherwise, express the area of the circle in square millimetres.  (1 mark)
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Volume, SM-Bank 066

Gavin is going camping in the summer holidays and purchased the two-person tent shown below.

  1. Given the triangular face of the tent is isosceles, use Pythagoras' Theorem to calculate the perpendicular height of the tent.  (2 marks)
  2. Using your answer from (a), calculate the volume of the tent in cubic metres.  (2 marks)
  3. What is the capacity of the tent in litres?  (1 mark)
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Volume, SM-Bank 065

  1. Given the triangular face of the prism above is isosceles, use Pythagoras' Theorem to calculate its perpendicular height. Give your answer correct to the nearest whole centimetre.  (2 marks)
  2. Using your answer from (a), calculate the volume of the prism in cubic centimetres.  (2 marks)
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Volume, SM-Bank 064

  1. For the triangular prism above, use Pythagoras' Theorem to calculate the perpendicular height, , of the triangular face.  (2 marks)
  2. Using your answer from (a), calculate the volume of the prism in cubic millimetres.  (2 marks)
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Volume, SM-Bank 060

A children's rectangular swimming pool measures 175 cm × 180 cm × 30 cm.

  1. Find the volume of the swimming pool in cubic centimetres.  (2 marks)

  2. What is the capacity of the swimming pool in litres?  (1 mark)

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Volume, SM-Bank 059

During the construction of a new house a concrete slab in the shape of a rectangular prism is to be poured.

The slab measures 20 m × 15 m × 0.15 m.

  1. Find the volume of the concrete required for the slab in cubic metres.  (2 marks)

  2. Calculate the cost of the concrete if it costs $350 per cubic metre.  (2 marks)

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Volume, SM-Bank 058

A rectangular sand pit measures 150 cm × 200 cm × 45 cm.

  1. Find the volume of the sand pit in cubic centimetres.  (2 marks)

  2. How many cubic metres of sand will the sand pit hold?  (1 mark)

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Volume, SM-Bank 047

A shipping container in the shape of a rectangular prism is being transported by truck to a construction site.

The dimensions of the container are marked on the diagram below and are in metres.
 

  1. Calculate the volume of the shipping container in cubic metres.   (2 marks)

  2. The shipping container is to be converted into a small lap pool on site.
    Calculate the capacity of the lap pool when full, giving your answer in kilolitres?       (1 mark)

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