Secondary 3 G2 Mathematics Tutor Bukit Timah | Surface Area and Volume: Unit Conversions. Did you know? Doubling a solid’s length scale can multiply its volume by eight.
This Secondary 3 G2 Mathematics tutor guide for Bukit Timah families explains surface area and volume: unit conversions using worked examples and practical checking habits. Follow the child’s school chapter list to choose the relevant questions.
Length, area and volume
Length uses units such as cm, area cm² and volume cm³. The exponents indicate how many dimensions are multiplied.
To confirm understanding, change the given values and solve independently. Explain why the same relationship applies, and check the original restrictions, units or data.
Cubic conversions
1 m=100 cm, so 1 m³=100³ cm³=1,000,000 cm³.
To confirm understanding, change the given values and solve independently. Explain why the same relationship applies, and check the original restrictions, units or data.
Litres and cubic centimetres
1 litre=1000 cm³. A 2.5 L container has capacity 2500 cm³.
To confirm understanding, change the given values and solve independently. Explain why the same relationship applies, and check the original restrictions, units or data.
Cuboid example
A cuboid 8 cm by 5 cm by 3 cm has volume 8×5×3=120 cm³.
To confirm understanding, change the given values and solve independently. Explain why the same relationship applies, and check the original restrictions, units or data.
Cuboid surface area
Its total surface area is 2(8×5+8×3+5×3)=2(40+24+15)=158 cm².
To confirm understanding, change the given values and solve independently. Explain why the same relationship applies, and check the original restrictions, units or data.
Scaling
If all cuboid dimensions double, surface area becomes four times and volume eight times the original.
To confirm understanding, change the given values and solve independently. Explain why the same relationship applies, and check the original restrictions, units or data.
Cylinder example
A cylinder of radius 3 cm and height 10 cm has volume πr²h=90π cm³, about 283 cm³.
To confirm understanding, change the given values and solve independently. Explain why the same relationship applies, and check the original restrictions, units or data.
Check
Do not convert cm² to m² using a length factor of 100; the area factor is 10000. Volume uses a factor of one million.
To confirm understanding, change the given values and solve independently. Explain why the same relationship applies, and check the original restrictions, units or data.
Seven-day revision plan
Day 1: identify the definitions. Day 2: reproduce one worked example. Day 3: change the numbers. Day 4: solve an unlabelled problem. Day 5: identify the first mistaken step. Day 6: combine this skill with a related chapter. Day 7: complete an independent retest after a delay.
Frequently asked questions
What should I do first? Identify what is known and what the question asks. How can I check my answer? Substitute into the original expression or data and verify the units. Why might an answer look correct but fail? A denominator restriction, unit conversion or interpretation can be wrong even when arithmetic is neat.
Official syllabus and small-group tutorial context
Consult the 2027 SEC G2 Mathematics K210 syllabus for the precise assessment scope. The unchanged eduKateSG Mathematics tutorial reference describes three-pupil small-group teaching near Sixth Avenue. Confirm current Secondary 3 G2 tutor, fees, venue, class fit and timetable directly.
Related Secondary 3 G2 Mathematics guides
See Direct and Inverse Proportion, Algebraic Expansion and Box Plots and Quartiles.