Olympiad Mathematics - Visualising Solid Shapes
Exam Duration: 45 Mins Total Questions : 30
Which of the following figures has six faces?
- (a)
- (b)
- (c)
- (d)
The number of faces of a cube is 6.
How many triangles can be seen in this figure?
- (a)
3
- (b)
5
- (c)
6
- (d)
7
The five triangles are, APQ, QXR, PZB, ABC and XYZ.
Which of the following pair of shapes, when joined together (by placing them edge to edge) can form a rectangle?
- (a)
- (b)
- (c)
- (d)
Clearly, the two halves of the rectangles when joined edge to edge form a rectangle.
Which of the following is different from the other three?
- (a)
- (b)
- (c)
- (d)
This figure has 5 lines unlike all other figures which have four sides.
How many corners does the shape given have?
- (a)
6
- (b)
10
- (c)
12
- (d)
13
Identify the correct statement from the following.
- (a)
A triangle has 3 sides and 4 vertices.
- (b)
A cylinder has 3 faces.
- (c)
All sides of the rectangle are equal.
- (d)
A cuboid has 4 flat faces and 12 straight edges.
Match the following.
- (a)
(i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
- (b)
(i)-(d), (ii)-(a), (iii)-(b), (iv)-(c)
- (c)
(i)-(c), (ii)-(b), (iiii)-(a), (iv)-(d)
- (d)
(i)-(d), (ii)-(a), (iii)-(c), (iv)-(b)
What is the number on the face opposite to 5 on a die?
- (a)
1
- (b)
2
- (c)
3
- (d)
6
The number on opposite faces of a die add up to 7. So, the number on the face opposite to 5 is 2.
The oblique sketch of 3 dice each with 2 cm edge placed side by side is given. What are its respective length, breadth and height?
- (a)
6 cm, 2 cm, 2 cm
- (b)
6 cm, 4 cm, 2 cm
- (c)
4 cm, 6 cm, 2 cm
- (d)
2 cm, 4 cm, 6 cm
The height and width ofthe cuboid formed by placing 3 dice remain the same. Only length will be tripled.
A die is cut horizontally. What is the crosssection obtained?
- (a)
A triangle
- (b)
A rectangle
- (c)
A square
- (d)
A cube
The cross section of a cube is a square.
The following figure shows a source of light (L), a solid (S)and its shadow (P) on a screen (M).
What is the shape of P?
- (a)
A rectangle
- (b)
A sphere
- (c)
A circle
- (d)
A triangle
The 2-D image of a sphere (ball) is a circle.
The shadow of a 3-D object is given.
Which of following could the object be?
- (a)
A book
- (b)
A ball
- (c)
A die
- (d)
A pipe
A book is cuboidal whose shadow is a rectangle.
The following is the shadow of a 3-D object
Which of these objects does the shadow belong to?
- (a)
- (b)
- (c)
- (d)
The pipe is cylindrical whose shadow is circular (front view).
Which of the following is a part of the front view of a honey comb?
- (a)
- (b)
- (c)
- (d)
A honey comb has a combination of hexagonal shapes when seen from the front.
Identify the front view of the object given.
- (a)
- (b)
- (c)
- (d)
The front view of the given object (as seen from the arrow) is a circle.
A hollow pipe is viewed from the side indicated by the arrow. In which shape is it?
- (a)
A ring
- (b)
A circle
- (c)
A cylinder
- (d)
An ellipse
From the side indicated by the arrow, the pipe looks like a ring.
The following arrangement of cubes is painted blue on all sides
How many square faces are painted blue?
- (a)
16
- (b)
9
- (c)
18
- (d)
12
Viewing the visible faces of the arrangement that are painted, we get 18.
In other words, 6 common faces of the 4 cubes are hidden. So the number of sides of the cube painted = 4 \(\times\) 6 - 6 = 24 - 6 = 18.
Which of these is the difference between a cube and a cuboid?
- (a)
There is no difference between a cube and cuboid.
- (b)
A cube has equal length, breadth and height where as a cuboid has different measuresfor length, breadth and height
- (c)
A cube has unequal length, breadth and height and a cuboid has equal length breadth and height.
- (d)
Either (A) or (C).
Option (B) gives the correct difference of a cube & a cuboid.
Which of the given geometric solids has the maximum number of vertices?
- (a)
Cone
- (b)
Cylinder
- (c)
Cuboid
- (d)
Pyramid
A cuboid has 8 vertices, which is the maximum number of vertices of the given figures.
If two cubes of dimensions 3 cm by 3 cm by 3 cm are placed side by side, what would the dimensions of the resulting cuboid be?
- (a)
6 cm \(\times\) 6 cm \(\times\) 6 cm
- (b)
12 cm \(\times\) 12 cm \(\times\) 12 cm
- (c)
9 cm \(\times\) 6 cm \(\times\) 3 cm
- (d)
6 cm \(\times\) 3 cm \(\times\) 3 cm
The two cubes of given dimensions when placed side by side result in a cuboid as shown in the figure. It has a length 6 cm, width 3 cm and height 3 cm.
What solid do you get when you give a vertical cut of a brick of dimensions 5 cm \(\times\) 5 cm \(\times\) 10 cm along 10 cm side?
- (a)
A cuboid
- (b)
A cylinder
- (c)
A cube
- (d)
A triangle
The brick of given dimensions is cut along the 10 cm side which results in a cuboid.
What is the shape formed by rotating a right triangle about its height?
- (a)
A sphere
- (b)
A cylinder
- (c)
A cone
- (d)
A cuboid
The right angled triangle PQR when rotated about its height results in a cone.
The top view and the front view of a solid are given in the figure.
Identify the solid.
- (a)
A cylinder
- (b)
A cone
- (c)
A prism
- (d)
A pyramid
Identify the net of the given solid.
- (a)
- (b)
- (c)
- (d)
The given solid has a triangular base and 3 triangular faces.
Identify the solid with 3 rectangular and 2 triangular faces, from the following.
- (a)
- (b)
- (c)
- (d)
The solid in option (C) has 3 rectangular and 2 triangular faces.
How many faces does this solid have?
- (a)
1
- (b)
2
- (c)
3
- (d)
4
The figure shows a solid. Which of the following is NOT the net of the given solid?
- (a)
- (b)
- (c)
- (d)
How many unit cubes were removed from the solid on the left to obtain the solid on the right?
- (a)
3
- (b)
4
- (c)
5
- (d)
6
Which of the following solids has the greatest number of faces?
- (a)
- (b)
- (c)
- (d)
(A) Number of faces = 14
(B) Number of faces = 10
(C) Number of faces = 8
(D) Number of faces = 12
How many faces, edges and vertices respectively does the given solid have?
- (a)
8,12,18
- (b)
10,18,12
- (c)
8,18,12
- (d)
10,12,18
Number of faces = 8
Number of edges = 18
Number of vertices = 12