11+ Entrance Non-Verbal Reasoning: 3D Shapes Questions and Answers — Questions and Answers
Question 1: A 2D net of a cube is shown. The faces have a circle, a square, and a triangle. The square is in the centre. The circle is on the face above the square, and the triangle is on the face to the right of the square. Which of the following cubes can be made by folding this net?
- {"answer":"A cube showing the square on the front, the circle on the top, and the triangle on the right face.","image":null} (Correct answer)
- {"answer":"A cube showing the square on the front, the triangle on the top, and the circle on the right face.","image":null}
- {"answer":"A cube showing the circle and the square on adjacent faces, with the triangle on the opposite face to the square.","image":null}
- {"answer":"A cube showing the square on the front, the circle on the top, and the triangle on the left face.","image":null}
Correct answer: {"answer":"A cube showing the square on the front, the circle on the top, and the triangle on the right face.","image":null}
When the net is folded, the square forms the front face. The face above it (the circle) will fold to become the top face. The face to the right (the triangle) will fold to become the right-hand face. The other options show incorrect orientations that are not possible from this net.
Question 2: A 3D shape is constructed by stacking identical cubes on a flat surface. The front view shows a stack of 3 cubes, a stack of 2 cubes, and a stack of 1 cube from left to right. The side view from the right shows a single column of 3 cubes. What is the minimum number of cubes needed to build this shape?
- {"answer":"8","image":null}
- {"answer":"6","image":null} (Correct answer)
- {"answer":"7","image":null}
- {"answer":"9","image":null}
Correct answer: {"answer":"6","image":null}
The front view tells us there are three columns with heights 3, 2, and 1. This accounts for 3 + 2 + 1 = 6 cubes. The side view from the right tells us the maximum height is 3 and the shape is only one cube deep from that perspective. Therefore, no cubes are hidden behind the visible ones from the front. The minimum number of cubes is 6.
Question 3: An L-shaped 3D object is made from four cubes in a line, with one additional cube placed on top of the second cube from the end. An arrow indicates you are looking at the object from the front. Which of the options correctly shows the view of the object from the right-hand side?
- {"answer":"A single column of two cubes.","image":null} (Correct answer)
- {"answer":"A shape like the letter 'T'.","image":null}
- {"answer":"A single column of three cubes.","image":null}
- {"answer":"A horizontal row of four squares.","image":null}
Correct answer: {"answer":"A single column of two cubes.","image":null}
The object is four cubes long and one cube deep. The maximum height is two cubes (at the position of the second cube from the end). When viewed from the right-hand side, you would see the end of the four-cube line (one cube) and the cube on top of it. This creates a single column that is two cubes high.
Question 4: A 3D shape is shown, which has a grey cylinder as a base and a white cone on top. Which of the options below shows the same shape after it has been rotated 90 degrees forward (top towards you)?
- {"answer":"The same shape, but with a grey cone and a white cylinder.","image":null}
- {"answer":"The shape lying on its side, with the grey circular base of the cylinder facing you and the white cone point to the right.","image":null}
- {"answer":"The shape is upside down, with the white cone at the bottom and the grey cylinder on top.","image":null}
- {"answer":"The shape lying on its side, with the white cone point facing you and the grey cylinder extending behind it.","image":null} (Correct answer)
Correct answer: {"answer":"The shape lying on its side, with the white cone point facing you and the grey cylinder extending behind it.","image":null}
Rotating the shape 90 degrees forward means tilting the top of the shape towards the viewer. The tip of the white cone, which was pointing up, will now be pointing directly at you. The grey cylinder will be positioned horizontally behind the cone.
Question 5: A pile of cubes is shown. The bottom layer is a solid 3x3 square of cubes. The second layer is a 2x2 square of cubes centred on top of the bottom layer. The top layer is a single cube placed in the centre of the second layer. How many cubes are in the pile in total?
- {"answer":"13","image":null}
- {"answer":"9","image":null}
- {"answer":"14","image":null} (Correct answer)
- {"answer":"10","image":null}
Correct answer: {"answer":"14","image":null}
To find the total number of cubes, calculate the number in each layer and add them together. The bottom layer is 3x3 = 9 cubes. The middle layer is 2x2 = 4 cubes. The top layer is 1 cube. The total is 9 + 4 + 1 = 14 cubes.
Question 6: Two 3D shapes are shown: a triangular prism and a cube of the same width. Which of the following shapes can be made by joining these two shapes together on one of their square faces?
- {"answer":"A larger cube.","image":null}
- {"answer":"A shape resembling a house with a pitched roof.","image":null} (Correct answer)
- {"answer":"A hexagonal prism.","image":null}
- {"answer":"A square-based pyramid.","image":null}
Correct answer: {"answer":"A shape resembling a house with a pitched roof.","image":null}
Placing the triangular prism on top of the cube, with the square face of the prism on the top square face of the cube, creates a shape that looks like a simple house. The cube forms the main body and the triangular prism forms the roof. The other options cannot be formed from these two components.
11+ Entrance Non-Verbal Reasoning: 3D Shapes Questions and Answers
A 2D net of a cube is shown.
The faces have a circle, a square, and a triangle.
The square is in the centre.
The circle is on the face above the square, and the triangle is on the face to the right of the square.
Which of the following cubes can be made by folding this net?