Free Mensa IQ Spatial Visualization Practice Test

Question 1

A cube has 6 faces. If you paint the outside of the cube and then cut it into 27 equal smaller cubes, how many small cubes have exactly 2 painted faces?

Accepted Answer

B. 12

Answer

When a cube is cut into 3×3×3=27 pieces: 8 corner pieces have 3 painted faces. 12 edge pieces (but not corners) have exactly 2 painted faces. 6 face-center pieces have 1 painted face. 1 center piece has 0.

Question 2

How many faces does a regular octahedron have?

Accepted Answer

B. 8

Answer

A regular octahedron has 8 equilateral triangular faces. It looks like two square pyramids joined at their bases.

Question 3

A rectangular box is 4 cm long, 3 cm wide, and 2 cm tall. What is the length of the diagonal that runs from one corner to the opposite corner through the interior?

Accepted Answer

C. √29 cm

Answer

Space diagonal = √(l²+w²+h²) = √(16+9+4) = √29 cm.

Question 4

If you fold a square piece of paper in half diagonally, then fold it in half again, what shape do you get?

Accepted Answer

C. Right triangle

Answer

Folding a square diagonally gives a right isosceles triangle. Folding that triangle again (along the altitude) gives a smaller right triangle.

Question 5

A cylinder has radius 3 cm and height 10 cm. How many times larger is its volume than a cone with the same radius and height?

Accepted Answer

B. 3 times

Answer

Cylinder volume = πr²h. Cone volume = (1/3)πr²h. Ratio = πr²h ÷ (1/3)πr²h = 3. The cylinder is exactly 3 times larger.

Mensa Practice Test Practice Test

Mensa Practice Test Practice Test

Free Mensa IQ Spatial Visualization Practice Test