IMO Practice Test — Volume
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
A rectangular prism has volume 480 cm³. If l=12 cm and h=5 cm, find w
6 cm
8 cm
10 cm
4 cm
Explanation: 480÷(12×5)=480÷60=8 cm
Question 2 of 6
hard
Two cubes: Cube A side 3 cm, Cube B side 4 cm. How many times larger is B's volume?
1.78×
2.37×
2×
1.5×
Explanation: A=27, B=64, 64÷27≈2.37
Question 3 of 6
hard
Irregular shape: heights: [3,2,1; 2,1,0; 1,0,0]. Total cubes?
10
12
15
18
Explanation: Sum: 3+2+1+2+1+0+1+0+0 = 10
Question 4 of 6
hard
A fish tank holds 20 L of water (1 L = 1000 cm³). Base is 50 cm × 40 cm. Find the height.
10 cm
20 cm
5 cm
15 cm
Explanation: 20 L = 20,000 cm³. Base area = 50×40 = 2000 cm². Height = 20000÷2000 = 10 cm
Question 5 of 6
hard
A rectangular prism has volume 1 m³. If l=1 m, w=1 m, find h in cm.
100 cm
10 cm
1000 cm
50 cm
Explanation: V=l×w×h → 1=1×1×h → h=1 m = 100 cm
Question 6 of 6
hard
How many 2 cm cubes can fit in a box 10 cm × 8 cm × 6 cm?
120
60
240
48
Explanation: Box volume=480 cm³, small cube=8 cm³, 480÷8=60