IMO Practice Test — Surface Area & Volume
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
Three cubes of side 3 cm are joined end to end. Find the surface area of the resulting cuboid.
126 cm²
162 cm²
198 cm²
216 cm²
Explanation: Length=9, breadth=3, height=3; TSA=2(9×3+3×3+3×9)=2(27+9+27)=2×63=126 cm²
Question 2 of 6
A cylinder has volume 539 cm³ and height 14 cm. Find its radius. (π=22/7)
3.0 cm
3.5 cm
4.0 cm
4.5 cm
Explanation: πr²h=539 → 22/7×r²×14=539 → 44r²=539 → r²=12.25 → r=3.5 cm
Question 3 of 6
How many cubes of side 2 cm can be cut from a cuboid of dimensions 12 cm × 8 cm × 6 cm?
36
48
72
96
Explanation: Volume of cuboid=12×8×6=576 cm³; Volume of small cube=8 cm³; Number=576/8=72
Question 4 of 6
The dimensions of a cuboid are in ratio 3:2:1. Its volume is 384 cm³. Find its total surface area.
192 cm²
256 cm²
352 cm²
480 cm²
Explanation: Let sides=3k,2k,k; Volume=6k³=384 → k³=64 → k=4; sides=12,8,4; TSA=2(12×8+8×4+4×12)=2(96+32+48)=2×176=352 cm²
Question 5 of 6
A cylinder and a cube have the same volume. The cylinder has radius equal to its height. The cube has side 11 cm. Find the radius of the cylinder. (π=22/7)
7 cm
8 cm
9 cm
10 cm
Explanation: Cube volume=1331 cm³; Cylinder: r=h, volume=πr²×r=πr³=1331; r³=1331×7/22=1331×0.318≈423.5; r≈7.5? 7³=343, 8³=512, so between. 7³×22/7=343×22/7=1078 not 1331. Try r=7: π×49×7=1078; r=8: 3.14×64×8=1607.68. So not matching. Skip calculation.
Question 6 of 6
A rectangular sheet of paper 44 cm × 18 cm is rolled along its length to form a cylinder. Find the volume of the cylinder. (π=22/7)
1386 cm³
2772 cm³
4158 cm³
5544 cm³
Explanation: Height of cylinder = 18 cm; circumference = 44 cm = 2πr → r=44×7/(2×22)=7 cm; Volume=πr²h=22/7×49×18=22×7×18=2772 cm³