KS3 Maths · Year 8 · Chapter 12: Compound units · Lesson 2

More compound units

Year 8About 75 minutesCalculator allowed48 marks

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Date

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Quick questions to start.

A1
Needed today
Work out the volume of a cuboid $5$ cm by $4$ cm by $3$ cm.
[1 mark]
Answer
A2
Needed today
How many cm³ are there in $2.5$ litres?
[1 mark]
Answer
A3
Last lesson
A car travels $150$ km in $2$ hours $30$ minutes. Work out its average speed.
[1 mark]
Answer
A4
Year 7
Work out the area of a circle of radius $3$ cm. Give your answer to $1$ decimal place.
[1 mark]
Answer

Example, then your turn

Year 8

Rate of flow $=$ quantity $\div$ time. Density $=$ mass $\div$ volume. Your teacher works through each example with you. Then try the one beside it.

Example 1

A tap fills a $24$ litre bucket in $3$ minutes. Work out the rate of flow.

Hint Rate of flow

=

quantity

\div

time. Litres and minutes give litres per minute.

B1
A hose puts $130$ litres of water into a pond in $4$ minutes. Work out the rate of flow.
[2 marks]
Answer $\dots$ litres per minute

Example 2

Water flows into a tank at $12$ litres per minute. How long does it take to put $300$ litres into the tank?

Hint Time

=

quantity

\div

rate.

B2
A pump empties a pond at $45$ litres per minute. The pond holds $3150$ litres. How long does the pump take to empty it? Give your answer in hours and minutes.
[3 marks]
Answer $\dots$ hour $\dots$ minutes

Example 3

A fountain pumps $4$ litres of water every second. Write this rate in litres per minute and in m³ per hour.

Hint There are

60

seconds in a minute and

3600

seconds in an hour.

1

m³

= 1000

litres.

B3
Water flows through a pipe at $2.5$ litres per second. Write this rate in litres per minute and in m³ per hour.
[3 marks]
Answer $\dots$ litres per minute, $\dots$ m³ per hour

Example 4

A block of metal has a mass of $540$ g and a volume of $60$ cm³. Work out its density.

Hint Density

=

mass

\div

volume. Grams and cm³ give g/cm³.

B4
A stone has a mass of $351$ g and a volume of $135$ cm³. Work out its density.
[2 marks]
Answer $\dots$ g/cm³

Example 5

A wooden block is a cuboid. Its density is $0.7$ g/cm³. Work out its mass.

Not drawn accurately

Hint Find the volume first. Then mass

=

density

\times

volume.

B5
A glass block is a cuboid. The density of the glass is $2.5$ g/cm³. Work out the mass of the block.
[3 marks]
Not drawn accurately
Answer $\dots$ g

Practice

Year 8

C1
Silver has a density of $10.5$ g/cm³. A silver bracelet has a mass of $63$ g. Work out its volume.
[2 marks]
Answer $\dots$ cm³
C2
A liquid has a density of $1.26$ g/cm³. Write this density in kg/m³.
[2 marks]
Answer $\dots$ kg/m³

C3
The table shows the mass and the volume of three blocks. Which block has the greatest density? Show how you decide.
[3 marks]
C4
A cable has a mass of $0.15$ kg per metre. A full roll of the cable has a mass of $18$ kg. How many metres of cable are on the roll?
[2 marks]
Answer $\dots$ m
C5
A dripping tap loses $25$ ml of water every minute. How many litres does it lose in one day?
[3 marks]
Answer $\dots$ litres

Exam-style questions

GCSE Foundation

D1
A block of plastic has a mass of $300$ g and a volume of $375$ cm³. Jo says: "The density of the plastic is $1.25$ g/cm³."
Explain what Jo has done wrong. Work out the correct density.
[3 marks]

D2
A solid cylinder is made of aluminium. The density of aluminium is $2.7$ g/cm³. Work out the mass of the cylinder. Give your answer to the nearest gram.
[4 marks]
Not drawn accurately
Answer $\dots$ g
D3
A fish tank is a cuboid. It is empty. Water is put into the tank from a hose at $8$ litres per minute. $1$ litre $= 1000$ cm³.
Not drawn accurately
(a)
How many litres does the tank hold when it is full?
[2 marks]
Answer $\dots$ litres
(b)
The tank is filled until the water is $5$ cm below the top. How long does this take? Give your answer in minutes and seconds.
[3 marks]
Answer $\dots$ minutes $\dots$ seconds
Total for D3: 5 marks
D4
Pressure $=$ force $\div$ area. A box has a weight of $360$ N. It rests on the floor on its face $0.4$ m by $0.3$ m. Then it is turned so that it rests on its face $0.3$ m by $0.2$ m. How much does the pressure on the floor increase? Give the units of your answer.
[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 tank holds $360$ litres. Tap A on its own fills the empty tank in $30$ minutes. Tap B on its own fills it in $45$ minutes. Both taps are turned on together. How long does it take to fill the empty tank?
[3 marks]
Hint 1 · What to try
Work out the rate of flow of each tap, in litres per minute.
Hint 2 · The first line
Tap A gives $12$ litres per minute and tap B gives $8$ . Together they give $20$ litres per minute.
Hint 3 · The full method
$360 \div 20$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out a rate of flow, and a time from a rate.
I can change a rate or a density into different units.
I can work out a density, a mass or a volume.
I can use density with the volume of a cuboid or a cylinder.

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