Tube, tin and box: volume and surface problems
Roll a sheet into a tube and give its capacity in litres, compare the sheet needed for a tin and a box, and find the volume of an open box.
- Iran: grade 7
Guide
This studio follows the combined problems of the Iranian Grade 7 lesson on volume and surface. In these problems π is taken as 3. Volume of a cylinder: base area × height, that is 3×r×r×h.
If you roll a rectangle into a tube, one side goes round the circle (circumference 2×3×r) and the other side is the height. Rolling it the other way gives a different cylinder.
capacity is given in litres: 1 litre is 1000 cubic centimetres. To convert, divide the volume by 1000.
The total area of a cylinder: two bases and one rectangle (the label). The total area of a box: 6 faces. Less surface means less sheet.
If you cut a small square from each corner of a square card and fold up the sides, you get an open box. Bigger squares do not always give a bigger box.