Secondary 1 G1 Mathematics Tutor Bukit Timah. Did you know? An L-shaped solid’s volume can often be found by subtracting the missing block from a complete cuboid. This guide includes worked examples and a short home check.
Before calculating, identify what is still solid and what has been removed. The drawing tells you which three lengths belong together.
Did you know? A missing block changes the volume
Did you know? A solid may look like a large rectangular box but have a corner cut away. If you multiply only the outer dimensions, you have counted material that is no longer there. In Secondary 1 G1 Mathematics, a composite solid becomes easier when we identify the smaller cuboids making it up.
Start by asking: Which space is occupied and which space is empty? Mark the missing part before writing any formula. This is more useful than trying to memorise a different formula for every L-shaped drawing.
First understand the volume of a whole cuboid
The volume of a cuboid is length × width × height. A complete cuboid measuring 6 cm by 4 cm by 3 cm would have volume 6 × 4 × 3 = 72 cm³.
The cubic unit matters. It tells us we are measuring three-dimensional space, as though counting 72 little cubes of side 1 cm. If a learner writes 72 cm², the multiplication may be right but the quantity described is an area rather than a volume.
Before multiplying, check that the three lengths belong to one cuboid and use the same unit.
Worked example: subtract the rectangular cut-out
Imagine a fictional wooden block measuring 6 cm × 4 cm × 3 cm. A 2 cm × 2 cm × 3 cm section is removed from one corner, all the way through the 3 cm height. The top view of what remains is L-shaped.
The complete block has volume 72 cm³. The missing piece has volume 2 × 2 × 3 = 12 cm³. Therefore the remaining volume is 72 − 12 = 60 cm³.
Notice why it was essential to know the third dimension of the cut-out. A 2 cm by 2 cm square on the top surface does not, by itself, tell us the depth of the missing three-dimensional region.
This is an invented teaching example, not a description of an actual object in Bukit Timah.
Check it another way: add the solid pieces
The same remaining L-shaped block can be divided into two non-overlapping cuboids. The first piece measures 4 cm × 4 cm × 3 cm, giving volume 48 cm³.
The second piece measures 2 cm × 2 cm × 3 cm, giving 12 cm³. Adding the pieces gives 48 + 12 = 60 cm³. This agrees with the subtraction method.
The second solution is a useful proof that the first calculation makes sense. It works because the pieces together cover all the material exactly once, without a gap or overlapping interior.
A pupil who draws overlapping pieces may accidentally count one region twice. Ask them to shade each part separately and state its dimensions.
Missing edge lengths: work them out before calculating volume
Some diagrams give the full length but not each small section. If the overall length is 6 cm and a retained section measures 4 cm along the same direction, the other section is 6 − 4 = 2 cm.
Label that missing value directly on the drawing. Repeat for width or height if needed. The three dimensions used for a particular volume must describe that same rectangular part.
Choosing the first three labels a pupil notices is not a method. The numbers must refer to three perpendicular directions of a cuboid.
What happens when the cut-out is shallower?
Keep the 6 cm × 4 cm × 3 cm outer block, but change the removed corner to 2 cm × 2 cm × 1 cm. Now the removed volume is 2 × 2 × 1 = 4 cm³, so the remaining volume is 72 − 4 = 68 cm³.
The answer is larger than 60 cm³ because less material was removed. Although the opening may look similar from above, the cut does not reach the full height.
This is a good test of understanding: if one dimension changes, should the missing volume stay the same? Of course not. Volume depends on all three dimensions.
Volume and surface area answer different questions
Volume asks how much three-dimensional material remains. Surface area asks how much of the outside faces is exposed. A cut-out always reduces material volume, but can reveal new inner faces.
Therefore, when finding surface area, you cannot usually subtract the entire surface area of the removed cuboid from that of the original block. Instead, identify the exposed faces of the resulting shape and count each once.
The words volume and surface area should trigger two different mental pictures: filled cubes for volume and outside panels for surface area.
What a small-group tutor should look for
A student may calculate the outer volume correctly but forget to subtract the missing region. Another may subtract 4 cm², which is an area, from 72 cm³, which is a volume. A third may add two overlapping parts and count material twice.
These are different reasoning errors. eduKateSG’s published Secondary 1 Mathematics tutorial model near Sixth Avenue MRT uses three-pupil groups and weekly 1.5-hour lessons, with close attention to student workings and guided correction.
A tutor can ask the learner to point to the existing and missing blocks, explain each dimension and solve the same shape a second way. The goal is independence when the next diagram looks unfamiliar.
Five-minute composite volume check
Question A: What is the volume of a 4 cm by 3 cm by 2 cm cuboid? Answer: 24 cm³.
Question B: A 1 cm by 1 cm by 2 cm block is removed. What volume remains? Answer: 24 − 2 = 22 cm³.
Question C: A 5 cm by 4 cm by 3 cm cuboid loses a 1 cm by 2 cm by 3 cm block. What volume remains? Answer: 60 − 6 = 54 cm³.
Ask the child to explain the subtraction and check that the result is smaller than the original volume. A sensible size-check often catches an error even before the working is marked.
Frequently asked questions
Are composite solids covered in Secondary 1 G1 Mathematics? Yes. The MOE G1 syllabus includes volume and surface area of composite solids.
Can I always subtract a cut-out from a large cuboid? When the complete outer cuboid and the removed three-dimensional block are defined correctly, subtracting their volumes gives the remaining volume.
Why might surface area be harder? Removing a block may uncover new faces, so surface area needs its own check of which faces are exposed.
Related G1 Mathematics guides
- Cube and Cuboid: Volume Versus Surface Area
- L-Shaped Perimeters
- Circle Circumference Versus Area
- Fractions, Decimals and Percentages
- Tally Marks and Frequency Tables
For the established teaching programme, see the original eduKateSG Secondary 1 Mathematics small-group tutorial guide. The reference page remains unchanged and describes three-pupil tutorials near Sixth Avenue MRT, with weekly 1.5-hour lessons and guided corrections.
For official subject scope, consult the Ministry of Education G1 Mathematics syllabus. G1 is a subject level under Full Subject-Based Banding and not the same as Posting Group 1. Schools may cover chapters in different sequences.
For Bukit Timah families: Bring a marked G1 Maths question to a parent-student consultation and identify where the working first becomes unclear. Enquire with eduKate Singapore about class suitability and availability.