The volume of a prism
Answers are for parents and teachers.
1
A pool measures 25 m × 10 m × 2 m. How many m³ of water does it hold and how many litres is that?
V = 500 m³ = 500,000 litres.
2
A cuboid has a rectangular base with sides 5 and 12 and a diagonal section of area 130. Find its volume.
The base diagonal is 13; 13 · h = 130 ⇒ h = 10; V = 60 · 10 = 600.
3
Are a cube of edge 3 and a cuboid 1 × 3 × 9 equivalent? Are they congruent?
Both volumes are 27, so they are equivalent. Their shapes differ, so they are not congruent.
4
Find the volume of an oblique prism with a square base of side 6 and a lateral edge 12 inclined at 30° to the base.
h = 12 · 1/2 = 6; V = 36 · 6 = 216.
5
A 40 m × 15 m yard is covered with concrete 8 cm thick. What is the volume of concrete in m³?
48