Lesson 8 of 8 · Grades 3 to 6
Real-life area and volume problems
How much paint covers a wall? How much water fills a tank? How much fence goes around a garden? This lesson uses one method for perimeter, area and volume problems in the real world.
A four-step method
Word problems mix a story with a measurement, and the measurement tells you which rule to use. Work through four steps each time. Read the question. Decide whether it needs perimeter, area or volume. Compute with the matching rule. Label the answer with its unit.
The decision is the important part. Distance around an edge is perimeter. Flat surface is area. Space inside a container is volume. One word in the question, such as fence, paint or tank, usually points straight at the right choice.
Fencing and painting
A fence follows the edge of a garden, so it needs the perimeter. A patch of grass covers the inside, so it needs the area. A wall to paint is a flat surface, so it needs area as well. The same garden can use both measures in one problem, and the answer needs both units.
The wall below is 6 m long and 4 m tall, so its area is 6 × 4 = 24 m². If one tin of paint covers 12 m², then 24 ÷ 12 = 2 tins cover the wall. The perimeter of the wall is not needed, because paint covers the surface, not the edge.
Filling a tank
A water tank is a rectangular prism, so filling it needs volume. The tank below is 50 cm long, 30 cm wide and 40 cm tall. Its volume is 50 × 30 × 40 = 60,000 cm³. Because 1,000 cm³ is one litre, the tank holds 60,000 ÷ 1,000 = 60 litres of water.
This is where the unit changes matter. Water is often sold in litres, while the tank is measured in centimetres. Compute the volume first in cubic centimetres, then convert at the end. A quick estimate helps: 60 litres is about 12 large watering cans, which is sensible for a tank of that size.
Checking the answer
Finish every problem the same way. Check that the unit matches the question: metres for a fence, square metres for a floor, litres for water. Check that the size is sensible. A garden fence of 3 m is far too short, and a teacup does not hold 400 litres.
If the numbers look wrong, reread the question before you recompute. Many mistakes come from answering the perimeter when the question asked for the area, or from mixing centimetres and metres in one multiplication.
Worked example
A paddock is 25 m long and 12 m wide. How much fencing goes around it, and what is the grass area inside?
Step 1: read the question. Fencing goes around the edge, so it needs the perimeter. Grass fills the inside, so it needs the area.
Step 2: find the perimeter. 2 × (25 + 12) = 2 × 37 = 74 m of fencing.
Step 3: find the area. 25 × 12 = 300 m² of grass.
Step 4: label both answers with their units and check the sizes. 74 m of fence and 300 m² of grass are sensible for a paddock.
Answer: 74 m of fencing and 300 m² of grass.
Watch out for this
The word around means perimeter, the word cover means area, and the word fill means volume. Read the question twice and underline the clue. Then write the unit you expect before you compute, so the numbers have a target to hit.
Remember
- Read, choose the rule, compute, then label the unit.
- Perimeter for a fence, area for paint and tiles, volume for water and boxes.
- Convert units when the problem mixes them, and check the size at the end.
- 1,000 cm³ is 1 litre of water.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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A wall is 7 m long and 3 m tall. What is its area?
Show answer
21 m². 7 × 3 = 21.
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A garden is 10 m long and 6 m wide. How much fence goes around it?
Show answer
32 m. 2 × (10 + 6) = 32.
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A box is 30 cm long, 20 cm wide and 10 cm tall. What is its volume?
Show answer
6,000 cm³. 30 × 20 × 10 = 6,000.
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One tile covers 1 m². How many tiles cover a floor 9 m long and 4 m wide?
Show answer
36 tiles. The floor is 36 m², and each tile is 1 m².
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A tank holds 40 L. It already has 15 L inside. How many litres are needed to fill it?
Show answer
25 L. 40 - 15 = 25.
Puzzle · Fish tank
Puzzle time
A fish tank is 60 cm long, 30 cm wide and 40 cm tall. How many litres of water fill it? Use 1,000 cm³ = 1 litre.
Show a hint
Find the volume in cubic centimetres first, then divide by 1,000 to change it to litres.
Show the answer
Answer: 72 L. 60 × 30 × 40 = 72,000 cm³. Then 72,000 ÷ 1,000 = 72, so the tank holds 72 litres.