Compound solids, volume stories and a 3-D city
Answers are for parents and teachers.
1
A step is a block 10 × 4 × 2 with a second block 5 × 4 × 3 on top. Find the volume of the whole step.
10 × 4 × 2 = 80 and 5 × 4 × 3 = 60. 80 + 60 = 140 cm³.
2
A cube of side 6 cm has a smaller cube of side 2 cm cut out of one corner. What volume is left?
6 × 6 × 6 = 216 and 2 × 2 × 2 = 8. 216 − 8 = 208 cm³.
3
A water tank is 80 cm × 50 cm × 40 cm. How many litres does it hold?
80 × 50 × 40 = 160,000 cm³ = 160 litres.
4
How many cubes of side 5 cm fit in a box 30 cm × 20 cm × 10 cm?
30 ÷ 5 = 6, 20 ÷ 5 = 4, 10 ÷ 5 = 2. 6 × 4 × 2 = 48 cubes.
5
Design a tiny city of 3 buildings with a limit of 100 cubes. Write each building’s length, width, height and volume, and the total.
Answers vary. For example 5 × 4 × 2 = 40, 4 × 3 × 3 = 36 and 3 × 2 × 4 = 24; total 100, which fits the limit.