Free IST Spatial Reasoning Questions and Answers

Question 1

If a cube is painted on all six faces and then cut into smaller cubes, how many of the smaller cubes will have paint on exactly two faces?

Accepted Answer

12

Answer

Cubes with paint on exactly two faces are located along the edges of the original large cube, but not at the corners. A cube has 12 edges. If the large cube is cut into a 3x3x3 array of smaller cubes, each edge will have (3-2)=1 smaller cube with paint on exactly two faces. Therefore, 12 edges multiplied by 1 cube per edge equals 12 cubes.

Question 2

Which shape will the net of a cube form when folded?

Accepted Answer

Cube

Answer

A net is a two-dimensional pattern that can be folded to form a three-dimensional shape. The net of a cube is specifically designed with six square faces arranged in a way that, when folded along its edges, it perfectly encloses a space to create a cube. This is the fundamental definition and purpose of a cube's net.

Question 3

If a pyramid has a square base and is viewed from above, what shape will be visible?

Accepted Answer

Square

Answer

When a pyramid with a square base is viewed directly from above, the observer looks down onto its base. The apex (the top point) of the pyramid will appear as a central point, and the four triangular faces will converge towards it, but the outermost boundary of what is seen will be the square shape of its base.

Question 4

Which three-dimensional shape will you get if you rotate a rectangle around one of its sides?

Accepted Answer

Cylinder

Answer

When a rectangle is rotated around one of its sides, that side becomes the axis of rotation. The opposite side sweeps out a circular path, forming the top and bottom circular bases of the resulting three-dimensional shape. The other two sides of the rectangle trace out the curved lateral surface, thus creating a cylinder.

Question 5

If you have a solid block in the shape of a rectangular prism and you remove a smaller rectangular prism from one corner, how many faces will the resulting shape have?

Accepted Answer

7

Answer

A rectangular prism initially has 6 faces. When a corner is removed, for example by making a single planar cut (a truncation), one new face is created. The three original faces that met at the corner are reshaped, and the three faces opposite the corner remain untouched. This results in a total of 3 untouched faces + 3 reshaped original faces + 1 new face = 7 faces for the resulting shape.

IST - Industrial Skills Test Practice Test

IST - Industrial Skills Test Practice Test

Free IST Spatial Reasoning Questions and Answers