55
Chapter VI review problems
Textbook: Part 2, lesson 55, pp. 71–75
GoalReview of Chapter VI: polyhedra, surface area, volume, the link between volume and capacity.
New words
capacity · sig‘immillilitre (ml) · millilitr (ml)litre (l) · litr (l)surface area and volume · sirt yuzi va hajm
Explanation
Surface area is measured in square units (cm², dm²), while volume is measured in cubic units (cm³, dm³). For a rectangular parallelepiped S = 2(ab + bc + ac) and V = abc; for a cube S = 6a² and V = a³. For liquids 1 cm³ = 1 ml and 1 dm³ = 1 l. The mass of 1 ml of water is 1 g and of 1 l of water is 1 kg. So the capacity and mass of water are easy to find from the volume. When solving, first decide whether area or volume is asked for.
Worked examples
A container 20 cm by 10 cm by 5 cm: V = 20 · 10 · 5 = 1000 cm³ = 1000 ml = 1 l. Water filling it has mass 1 kg.
A pool 5 m by 3 m by 2 m: V = 30 m³ = 30 000 dm³ = 30 000 l.
Class activity
“What does a litre look like?”: with an adult's help, fill a 1-litre container with water and imagine a cube about 10 cm × 10 cm × 10 cm having the same volume.
Practice
1
An aquarium is 50 cm by 30 cm by 40 cm. How many litres does it hold (1 l = 1000 cm³)?
60
2
What is the mass (g) of water filling a cube-shaped vessel with edge 10 cm (1 cm³ of water = 1 g)?
1000
3
How many dm² must be painted on all faces of a cube with edge 3 dm?
54
4
Why is surface area measured in cm² and volume in cm³?
Area is two-dimensional (length × length), while volume is three-dimensional (length × length × length).