Mixed measurement applications | Year 8

01 / LEARN

Understand the idea.

Decide what the situation needs

Translate the situation into a measurement: edging needs boundary length, covering needs area, and filling needs volume or capacity. List the given dimensions and their units, then identify any radius or cross-sectional area that must be found first.

Keep linked calculations separate. For a partly filled tank, find its full internal volume, convert to the requested capacity unit, then take the stated fraction or percentage. Written units show when you have moved from area to volume to capacity.

Check the result before deciding

Use the context to make the final decision. A fractional number of boxes may be a correct division result, but buying enough material requires a whole number rounded up. A percentage allowance increases the required area before the package calculation.

Check that the result is reasonable and that the model fits the object. The prism formula assumes a constant cross-section. Capacity needs internal space; uneven depth or thick walls may require information beyond the measurements supplied.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

A partly filled tank

A tank has internal base area 5 m² and height 0.8 m. It is 75% full. How many litres of water does it contain?

Worked solution

1
Find the full internal volume.
$V = 5 \times 0.8 = 4 m^{3}$
Using the prism model, take the given base area as constant throughout the tank's height.
2
Express the full capacity in litres.
$4 \times 1000 = 4000 L$
One cubic metre holds one thousand litres.
3
Take the stated filled proportion.
$Water = \frac{75}{100} \times 4000 = 3000 L$
The water occupies 75 percent of the tank's full capacity.

Answer

3000 L.

EXAMPLE 02

Buying enough material

A rectangular floor is 4 m by 3 m. Tiles cover 0.5 m² per box. Allow 10% extra area for cutting. How many whole boxes are needed?

Worked solution

1
Calculate the floor area.
$A = 4 \times 3 = 12 m^{2}$
The floor is rectangular.
2
Add the cutting allowance.
$\begin{aligned} 10 % of 12 & = 1.2 m^{2} \\ Required area & = 12 + 1.2 = 13.2 m^{2} \end{aligned}$
The extra ten percent is based on the original floor area.
3
Divide by the coverage of one box.
$Boxes = \frac{13.2}{0.5} = 26.4$
Each box supplies half a square metre of tiles.
4
Choose enough whole boxes.
$26 (0.5) = 13 < 13.2, 27 (0.5) = 13.5 \geq 13.2$
Twenty-six boxes fall short, so the minimum purchase is 27 boxes.

Answer

27 boxes.

03 / YOUR TURN

Try it yourself.

Check your understanding

A tank’s full capacity is 800 L. It is one-quarter full. How much water is in it?

Show answer & reasoning

200 L.

One-quarter full means one of four equal shares of the capacity: $\frac{1}{4} \times 800 = 200 L$ . This is less than the full capacity, as expected.

Keep practising

6 worksheet questions · 18 marks

Open worksheet Worked solutions

Read the questions online

A rectangular bed is 6 m by 4 m. Soil is added to a uniform depth of 0.2 m. Find the soil volume.
3 marks
A 2 m³ tank is 60% full. Find the water volume in litres.
3 marks
A 3 m by 2 m rectangle is covered using sheets of area 0.8 m² each. Ignore overlap. Find the minimum number of whole sheets by area.
3 marks
A circular flowerbed has radius 2 m. A gardener doubles the radius. What happens to the area?
3 marks
A tank measures 1.2 m by 80 cm by 50 cm internally. Find its capacity in litres.
4 marks
A garden is shown only by a sketch with no scale or dimensions. Can its actual area be calculated? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A rectangular bed is 6 m by 4 m. Soil is added to a uniform depth of 0.2 m. Find the soil volume.
3 marks
Base area: $6 (4) = 24$ m².
Volume: $24 (0.2) = 4.8$ m³.
4.8 m³.
A 2 m³ tank is 60% full. Find the water volume in litres.
3 marks
Full capacity is 2000 L.
$0.60 (2000) = 1200$ L.
1200 L.
A 3 m by 2 m rectangle is covered using sheets of area 0.8 m² each. Ignore overlap. Find the minimum number of whole sheets by area.
3 marks
Area is 6 m².
$\frac{6}{0.8} = 7.5$ , so at least 8 whole sheets are needed by area.
8 sheets.
A circular flowerbed has radius 2 m. A gardener doubles the radius. What happens to the area?
3 marks
Old area is $4 π$ m².
New radius is 4 m, giving $16 π$ m².
The ratio is $\frac{16}{4} = 4$ .
It becomes four times as large.
A tank measures 1.2 m by 80 cm by 50 cm internally. Find its capacity in litres.
4 marks
Convert dimensions to metres: 1.2, 0.8 and 0.5.
Volume is $1.2 (0.8) (0.5) = 0.48$ m³.
Capacity is $0.48 (1000) = 480$ L.
480 L.
A garden is shown only by a sketch with no scale or dimensions. Can its actual area be calculated? Explain.
2 marks
The same sketch could represent gardens of many sizes.
Measurements from an unscaled drawing do not determine actual lengths.
No. A scale or sufficient actual dimensions are needed.

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Circumference and area of circles; perimeter/area of composite shapes; choosing and converting area units; cross-sections of prisms; prism volume and capacity; mixed measurement applications.

Official curriculum source ↗

In this lesson

Understand the idea.

Decide what the situation needs

Check the result before deciding

See the method in action.

A partly filled tank

Find the full internal volume.

Express the full capacity in litres.

Take the stated filled proportion.

Buying enough material

Calculate the floor area.

Add the cutting allowance.

Divide by the coverage of one box.

Choose enough whole boxes.

Try it yourself.

Check your understanding

Keep practising