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

b.    \(11\ \text{cm}^{2}\)

Show Worked Solution

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

b.    \(1100\ \text{mm}^{2}\) \(= \dfrac{1100}{100} \)
  \(=11\ \text{cm}^{2} \)

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

b.    \(95\ 000\ \text{mm}^{2}\)

Show Worked Solution

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

b.    \(900\ \text{cm}^{2}\) \(= 900 \times 100\ \text{mm}^{2} \)
  \(= 90\ 000\ \text{mm}^{2} \)

Unit Conversion, SM-Bank 013

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 square has an area of 125 square centimetres.
  2. Using the conversion equation, or otherwise, express the area of the rectangle in square millimetres.  (1 mark)
Show Answers Only

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

b.    \(12\ 500\ \text{mm}^{2}\)

Show Worked Solution

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

b.    \(125\ \text{cm}^{2}\) \(= 125 \times 100\ \text{mm}^{2} \)
  \(= 12\ 500\ \text{mm}^{2} \)

Unit Conversion, SM-Bank 004

The end of a cylinder has an area of 60 square millimetres.

Using the conversion ratio, 1 cm² = 100 mm², express this area in square centimetres.  (1 mark)

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\(0.6\ \text{cm}^{2}\)

Show Worked Solution
\(60\ \text{mm}^{2}\) \(= \dfrac{60}{100}\ \text{cm}^2\)  
  \(=0.6\ \text{cm}^{2}\)  

Unit Conversion, SM-Bank 003

One side of an Australian 10-cent coin has an area of 437 square millimetres.

Using the conversion ratio, 1 cm² = 100 mm², express this area in square centimetres.  (1 mark)

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\(4.37\ \text{cm}^{2}\)

Show Worked Solution
\(437\ \text{mm}^{2}\) \(= \dfrac{437}{100}\ \text{cm}^2\)  
  \(=4.37\ \text{cm}^{2}\)  

Unit Conversion, SM-Bank 002

A circle with radius 1 cm, has an area of \(\pi\) square centimetres.

Using the conversion ratio, 1 cm² = 100 mm², express the area of the circle in square millimetres.  (1 mark)

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\(100\pi\ \text{mm}^{2}\)

Show Worked Solution
\(\pi\ \text{cm}^{2}\) \(= \pi \times 100\ \text{mm}^2\)  
  \(=100\pi\ \text{mm}^{2}\)  

Unit Conversion, SM-Bank 001

A rectangle has an area of 450 square centimetres.

Using the conversion ratio, 1 cm² = 100 mm², express the area of the rectangle in square millimetres.  (1 mark)

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\(45\ 000\ \text{mm}^{2}\)

Show Worked Solution
\(450\ \text{cm}^{2}\) \(= 450 \times 100\ \text{mm}^{2} \)
  \(= 45\ 000\ \text{mm}^{2} \)

Area, SM-Bank 094

A poster has an area of 5250 square centimetres.

Find the area of the poster in square millimetres?   (2 marks)

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\(525\ 000\ \text{mm}^{2}\)

Show Worked Solution

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

\(\text{5250 cm}^{2} = 5250 \times 100 = 525\ 000\ \text{mm}^{2}\)

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 086

Convert an area of 500 square millimetres to square centimetres.  (1 mark)

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\(5\ \text{cm}^2\)

Show Worked Solution

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

\(500\ \text{mm}^2 =\dfrac{500}{100} =5\ \text{cm}^2\)

Area, SM-Bank 083

Convert an area of 3 square centimetres to square millimetres.   (1 mark)

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\(300\ \text{mm}^2\)

Show Worked Solution

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

\(\text{3 cm}^{2} = 3 \times 100 = 300\ \text{mm}^2\)

 

Area, SM-Bank 073 MC

A large square feature tile has an area of 15 625 square centimetres.

What is the area of the feature tile in square millimetres?

  1. \(156.25\ \text{square millimetres}\)
  2. \(1562.5\ \text{square millimetres}\)
  3. \(156\ 250\ \text{square millimetres}\)
  4. \(1\ 562\ 500\ \text{square millimetres}\)
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\(D\)

Show Worked Solution

\(\text{Side length}\ =\sqrt{15\ 625}\ =125\ \text{cm} = 125 \times 10 = 1250\ \text{mm}\)

\(\text{Area}\ =1250^2 =1\ 562\ 500\ \text{square millimetres}\)

\(\Rightarrow D\)

Area, SM-Bank 072 MC

A square table top has an area of 9025 square centimetres.

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

  1. \(9.025\ \text{square millimetres}\)
  2. \(90.25\ \text{square millimetres}\)
  3. \(90\ 250\ \text{square millimetres}\)
  4. \(902\ 500\ \text{square millimetres}\)
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\(D\)

Show Worked Solution

\(\text{Side length} =\sqrt{9025} =95\ \text{cm}= 95 \times 10 = 950\ \text{mm}\)

\(\text{Area}\ =950^2 =902\ 500\ \text{square millimetres}\)

\(\Rightarrow D\)