KS3 Maths · Year 7 · Chapter 6: Surface area and volume of prisms · Lesson 1

Metric units for area and volume

Year 7About 60 minutesCalculator allowed50 marks

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Date

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Quick questions to start.

A1
Needed today
Work out $4.7 \times 100$ .
[1 mark]
Answer
A2
Needed today
A cuboid measures $6$ cm by $5$ cm by $2$ cm. Work out its volume.
[1 mark]
Answer
A3
Last lesson
Triangles $A B C$ and $P QR$ are congruent, with $A$ matching $P$ and $B$ matching $Q$ . $A B = 9$ cm. Write down the length of $P Q$ .
[1 mark]
Answer
A4
From chapter 4
Work out $35%$ of $60$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Convert (a) $4.3$ cm² to mm² (b) $0.26$ m² to cm².

Hint

1

= 10

mm, so

1

cm²

= 10 \times 10 = 100

mm².

1

= 100

cm, so

1

m²

= 100 \times 100 = 10000

cm². A large unit to a small unit: multiply.

B1
Convert (a) $6.8$ cm² to mm² (b) $0.09$ m² to cm².
[2 marks]
Answer(a) $\dots\dots$ mm² (b) $\dots\dots$ cm²

Example 2

Convert (a) $7400$ mm³ to cm³ (b) $2300000$ cm³ to m³ (c) $650$ cm³ to litres.

Hint

1

cm³

= 1000

mm³,

1

m³

= 1000000

cm³ and

1

litre

= 1000

cm³. A small unit to a large unit: divide.

B2
Convert (a) $920$ mm³ to cm³ (b) $560000$ cm³ to m³ (c) $3800$ litres to m³.
[3 marks]
Answer(a) $\dots\dots$ cm³ (b) $\dots\dots$ m³ (c) $\dots\dots$ m³

Example 3

A rectangular field measures $160$ m by $95$ m. Work out its area in hectares.

Not drawn accurately

Hint Work out the area in m² first.

1

hectare

= 10000

m².

B3
A rectangular field measures $240$ m by $65$ m. Work out its area in hectares.
[2 marks]
Not drawn accurately
Answer

Example 4

A water tank is a cuboid. It is two-thirds full. Work out the number of litres of water in the tank.

Not drawn accurately

Hint Find the volume in m³, take two-thirds of it, then use

1

m³

= 1000

litres.

B4
A water tank is a cuboid. It is three-fifths full. Work out the number of litres of water in the tank.
[3 marks]
Not drawn accurately
Answer

Example 5

A rectangular floor is $3.6$ m by $2.4$ m. It is covered with square tiles of side $30$ cm. How many tiles are needed?

Not drawn accurately

Hint Change the floor's sizes into cm first, so both sizes are in the same unit.

B5
A rectangular floor is $4.5$ m by $3$ m. It is covered with square tiles of side $25$ cm. How many tiles are needed?
[3 marks]
Not drawn accurately
Answer

Practice

Year 7

C1
Which is larger, $0.48$ m² or $4500$ cm²? Show how you decide.
[2 marks]
Answer
C2
The diagram shows a cube with edges of $1$ cm. Explain why $1$ cm³ $= 1000$ mm³.
[2 marks]

C3
Write these areas in order of size, smallest first: $0.7$ hectares, $6500$ m², $72000000$ cm².
[2 marks]
Answer
C4
A jug holds $1.35$ litres of juice. How many glasses that each hold $150$ cm³ can be filled from the jug?
[2 marks]
Answer
C5
A rectangular board is $2.5$ m long and $40$ cm wide. Work out its area (a) in cm² (b) in m².
[3 marks]
Not drawn accurately
Answer(a) $\dots\dots$ cm² (b) $\dots\dots$ m²
C6
A cube has edges of $4$ cm. Work out its volume in mm³.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Kai says, " $3$ m² is the same as $300$ cm², because there are $100$ cm in $1$ m."
Kai is wrong. Explain why, and write $3$ m² in cm².
[2 marks]
Answer $3$ m² $= \dots\dots$ cm²

D2
A fish tank is a cuboid. It is $60$ cm long, $35$ cm wide and $40$ cm high. The water in the tank is $30$ cm deep.
Not drawn accurately
(a)
Work out the volume of water in the tank. Give your answer in litres.
[3 marks]
Answer
(b)
More water is added until the water is $38$ cm deep. How many litres of water are added?
[2 marks]
Answer
Total for D2: 5 marks
D3
The diagram shows a field. It is a rectangle with a right-angled triangle on one end.
Not drawn accurately
(a)
Work out the area of the field. Give your answer in hectares.
[3 marks]
Answer
(b)
The field is sold for £ $8500$ per hectare. Work out the price of the field.
[2 marks]
Answer
Total for D3: 5 marks
D4
A path is made of concrete. It is $12$ m long, $90$ cm wide and $8$ cm deep. Concrete costs £ $110$ per m³. Work out the cost of the concrete for the path. You must show your working.
[4 marks]
Not drawn accurately
Answer

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A cube with edges of $1$ m is cut into small cubes with edges of $2$ cm. The small cubes are put in one straight line, touching. How long is the line? Give your answer in kilometres.
[4 marks]
Hint 1 · What to try
Work out how many small cubes fit along one edge of the big cube.
Hint 2 · The first line
$100 \div 2 = 50$ small cubes along each edge, so there are $50 \times 50 \times 50$ small cubes.
Hint 3 · The full method
$5 0^{3} = 125000$ cubes. The line is $125000 \times 2 = 250000$ cm $= 2500$ m $= 2.5$ km.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can convert between mm², cm², m² and hectares.
I can convert between mm³, cm³, m³ and litres.
I can use unit conversions to solve problems about fields, tanks and tiles.

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