The purpose of this activity is to support students in distinguishing between the surface area and volume of cuboids. Students use multiplicative methods for finding the measurements, and record the measurements using appropriate units (square centimetres (cm2) for surface area and cubic centimetres (cm3) for volume). Students also need to develop a sense of size for important multiples of these units, such as 1000cm3 and 100cm2.
If you have sufficient cubes, make all the 10 possible unique models (as above).
All these cuboids have the same volume. Do they have the same surface area?
Let students discuss the question and come to a consensus about surface areas.
Allocate the cuboids and ask the students to use their rulers and calculators to find the surface areas. Organise the data in a table, as shown below:
Dimensions (cm) | Calculation for surface area | Surface area (cm2) |
4x12x10 | 2x (4x12+4x10+12x10) | 416cm2 |
4x4x30 | 2x (4x4+4x30+4x30) | 512cm2 |
4x20x6 | 2x (4x20+4x6+20x6) | 448cm2 |
6x8x10 | 2x (6x8+6x10+8x10) | 376cm2 |
2x2x120 | 2x (2x2+2x120+2x120) | 968cm2 |
2x4x60 | 2x (2x4+2x60+4x60) | 736cm2 |
2x6x40 | 2x (2x6+2x40+6x40) | 664cm2 |
2x8x30 | 2x (2x8+2x30+8x30) | 632cm2 |
2x10x24 | 2x (2x10+2x24+10x24) | 616cm2 |
2x12x20 | 2x (2x12+2x20+12x20) | 608cm2 |
Next steps
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/working-volume-and-surface-area-together at 9:03pm on the 26th February 2024