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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\(\pi\) square metres.
  2. Express this area in square centimetres, giving your answer in exact form.  (1 mark)
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a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(900\pi\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{0.09}\pi\ \text{m}^{2}\) \(= 0.09\pi \times 10\ 000 \)  
  \(=900\pi\ \text{cm}^2 \)

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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a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(26\ \text{m}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{265 000 cm}^{2}\) \(= \dfrac{26\ 000}{10\ 000}\)  
  \(=26\ \text{m}^{2}\)  

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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a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(750\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{0.075 m}^{2}\) \(=0.075 \times 10\ 000\)  
  \(=750\ \text{cm}^{2}\)  

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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a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(2\ 600\ 000\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{260 m}^{2}\) \(=260 \times 10\ 000\)  
  \(=2\ 600\ 000\ \text{cm}^{2}\)  

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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a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(20\ 106\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{Radius}\ =\dfrac{1.6}{2} = 0.8\ \text{m} \)

\(\text{Area}\) \(=\pi \times 0.8^2\)  
  \(=2.01061…\ \text{m}^{2}\)  
  \(=2.01061… \times 10\ 000\ \text{cm}^{2}\)  
  \(=20\ 106\ \text{cm}^{2}\)  

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)
Show Answers Only

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(20\ 000\ 000\ \text{mm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(2000\ \text{m}^{2}\) \(= 2000 \times 10\ 000\ \text{cm}^{2} \)
  \(= 20\ 000\ 000\ \text{cm}^{2} \)

Unit Conversion, SM-Bank 008

A circle has a radius of 60 centimetres.

Using the conversion ratio, 1 m² = 10 000 cm², or otherwise, calculate the exact area of the circle in square metres.  (2 marks)

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\(\ 0.36\pi\ \text{m}^{2}\)

Show Worked Solution
\(\text{Area}\) \(= \pi \times 60^{2}\)  
  \(=3600\pi\ \text{cm}^{2}\)  
  \(= \dfrac{3600}{10\ 000}\pi\ \text{m}^{2}\)  
  \(= 0.36\pi\ \text{m}^2 \)  

Unit Conversion, SM-Bank 007

A poster has an area of 2500 square centimetres.

Using the conversion ratio, 1 m² = 10 000 cm², express this area in square centimetres.  (1 mark)

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\(0.25\ \text{m}^{2}\)

Show Worked Solution
\(2500\ \text{cm}^{2}\) \(= \dfrac{2500}{10\ 000}\ \text{m}^2\)  
  \(=0.25\ \text{m}^{2}\)  

Unit Conversion, SM-Bank 006

Athletes throw shot puts from a shot put circle with a standard diameter of 2.13 metres.

Using the conversion ratio, 1 m² = 10 000 cm², or otherwise, calculate the area of a shot put circle to the nearest square centimetres.  (3 marks)

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\(8\ \text{cm}^{2}\)

Show Worked Solution

\(\text{Radius}\ = \dfrac{2.13}{2} = 1.065\ \text{m}\)

\(\text{Area}\) \(= \pi \times 1.065^{2}\)  
  \(=3.56327… \text{m}^{2}\)  
  \(=3.56327… \times 10\ 000\ \text{cm}^{2}\)  
  \(=35\ 633\ \text{cm}^2\ \ (\text{nearest cm}^2) \)  

Unit Conversion, SM-Bank 005

A pickleball court has an area of 81.74 square metres.

Using the conversion ratio, 1 m² = 10 000 cm², express this area in square centimetres.  (1 mark)

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\(817\ 400\ \text{cm}^{2}\)

Show Worked Solution
\(81.74\ \text{m}^{2}\) \(= 81.74 \times 10\ 000\ \text{cm}^2\)  
  \(=817\ 400\ \text{cm}^{2}\)  

Area, SM-Bank 089

Express an area of 0.003 square metres in square millimetres.  (2 marks)

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\(3000\ \text{mm}^2\)

Show Worked Solution

\(\text{1 m}^{2}\ =1000\ \text{mm}\times 1000\ \text{mm} =1\ 000\ 000\ \text{mm}^2\)

\(\text{0.003 m}^{2}\ = 0.003 \times 1\ 000\ 000 = 3000\ \text{mm}^{2} \)

Area, SM-Bank 087

A dining table has an area of 35 700 square centimetres.

Express this area in square metres.  (1 mark)

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\(3.57\ \text{m}^2\)

Show Worked Solution

\(\text{1 m}^{2}\ = 100\ \text{cm}\times 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

\(\text{35 700 cm}^{2} = \dfrac{35\ 700}{10\ 000} = 3.57\ \text{m}^2\)

Area, SM-Bank 084

Convert an area of 15 square metres to square centimetres.  (1 mark)

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\(150\ 000\ \text{cm}^2\)

Show Worked Solution

\(\text{1 m}^{2} = 100\ \text{cm}\times 100\ \text{cm}=10\ 000\ \text{cm}^2\)

\(\text{15 m}^{2}\ = 15 \times 10\ 000 = 150\ 000\ \text{cm}^2\)

Area, SM-Bank 082

Julia bought a kitchen rug with an area of 0.85 square metres.

What is the area of the kitchen rug in square centimetres?   (2 marks)

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\(8500\ \text{cm}^{2} \) 

Show Worked Solution

\(\text{1 m}^{2} = 100\ \text{cm} \times 100\ \text{cm}\ =10\ 000\ \text{cm}^{2} \)

\(\text{0.85 m}^{2} = 0.85 \times 10\ 000 = 8500\ \text{cm}^{2} \) 

Area, SM-Bank 081 MC

Ben bought a dog mat with an area of 0.5 square metres.

What is the area of the dog mat in square centimetres?

  1. \(2.5\ \text{cm}^2\)
  2. \(5\ \text{cm}^2\)
  3. \(5000\ \text{cm}^2\)
  4. \(25\ 000\ \text{cm}^2\)
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\(C\)

Show Worked Solution

\(\text{1 m}^{2} =100\ \text{cm}\times 100\ \text{cm} = 10\ 000\ \text{cm}^{2} \)

\(\text{0.5 m}^{2} = 0.5\times 10\ 000 =5000\ \text{cm}^2\)  

\(\Rightarrow C\)

Area, SM-Bank 077

Vlad has a giant chess board that has an area of 4 square metres.

What is the area of the chess board in square centimetres?  (2 marks)

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\(40\ 000\ \text{square centimetres}\)

Show Worked Solution

\(\text{Strategy 1 (convert square metres):}\)

\(\text{1 m}^{2} = 100\ \text{cm}\ \times 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2}\)

\(\text{Side length}\ =\sqrt{4} =2\ \text{m}\)

\(\text{Area}\ =2^2 = 4\ \text{m}\ = 4 \times 10\ 000 = 40\ 000\ \text{cm}^{2}\)
 

\(\text{Strategy 2 (convert sides to centimetres):}\)

\(\text{Side length}\ =\sqrt{4} =2\ \text{m}\ = 200\ \text{cm}\)

\(\text{Area}\ =200^2 = 40\ 000\ \text{square centimetres}\)

Area, SM-Bank 076

Jeremy's back deck is square in shape and has an area of 16 square metres.

What is the area of the deck in square centimetres?  (2 marks)

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\(160\ 000\ \text{square centimetres}\)

Show Worked Solution

\(\text{Strategy 1 (convert square metres):}\)

\(\text{1 m}^{2} = 100\ \text{cm}\ \times 100\ \text{cm}\ = 10\ 000\ \text{cm}^2 \)

\(\text{Side length of deck}\ =\sqrt{16} =4\ \text{m}\)

\(\text{Area} =4^2 = 16\ \text{m}^{2} = 16 \times 10\ 000 = 160\ 000\ \text{cm}^{2}\)
 

\(\text{Strategy 2 (convert side lengths):}\)

\(\text{Side length of deck}\ =\sqrt{16} =4\ \text{m}= 4 \times 100 = 400\ \text{cm}\)

\(\text{Area} =400^2 =160\ 000\ \text{cm}^{2}\)

Area, SM-Bank 074 MC

A square table top has an area of 4225 square centimetres.

What is the area of the table top in square metres?

  1. \(0.4225\ \text{square metres}\)
  2. \(4.225\ \text{square metres}\)
  3. \(42.25\ \text{square metres}\)
  4. \(42\ 250\ \text{square metres}\)
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\(A\)

Show Worked Solution

\(\text{Side length}\ =\sqrt{4225} =65\ \text{cm}= \dfrac{65}{10\ 000} = 0.65\ \text{m}\)

\(\text{Area}\ =0.65^2 =0.4225\ \text{square metres}\)

\(\Rightarrow A\)