Important Questions: Visualising Solid Shapes - Free MCQ Test with solutions

8 edges -4 sides of square and 4 sides of triangular faces,            

The number of faces on a cube is 6.

To elaborate:

• A cube has six flat surfaces.
• Each surface is a square.
• All faces are equal in shape and size.

Observe the given figures. In the figure in option [d], the shape is divided equally.    

This figure has 5 lines unlike all other figures which have four sides.    

To determine the possible shape of the solid object, consider the following observations:

• The object has a distinct top view and a side view.
• From the side, the shape appears to have a specific outline that must match the profiles of the potential options.
• From the top, the shape should also conform to the outline presented in the second image.

The analysis of the options reveals:

• Examine each option for correspondence with the side and top views.
• Identify any shapes that match the unique contours seen from both perspectives.

By cross-referencing the views with the options, the correct shape can be determined based on the matching characteristics. This methodical approach ensures that the chosen option accurately reflects the solid object in both views.

The shape in the image appears to be a star-like figure. By carefully counting the points where the lines meet, it can be seen that the shape has 12 corners.

 A cylinder has 3 faces  - two circular faces at the two ends and the third a curved face.

10 one-rupee coins piled up results in a cylinder.             

The number of vertices in a cube is 8.

The statement regarding the number of vertices in a cube is incorrect. Here are the details:

• A cube has 8 vertices.
• Each vertex is a point where three edges meet.
• This makes the cube a type of cuboid with equal edge lengths.

Thus, the correct information is that a cube contains 8 vertices, not 6.

(i)Since cylinder is made up of two circles and a rectangle it matches with (d)
(ii)Since cone is made up of one circle and a triangle it matches with (a)
(iii)Since cuboid is made up of 6 rectangles,it matches with (b)
(iv) Since square pyramid is made up of 4 triangles and a square it matches with (c)

A cube of edge 4 cm has square faces of side 4 cm.

The sum of numbers on opposite faces is 7. So, the total on the face opposite to 4+3  is 3+4=7

.

The number on opposite faces of a die add up to 7. So, the number on the face opposite to 5 is 2.

The height and width of the cuboid formed by placing 3 dice remain the same. Only length will be tripled.

The cross-section of a cube is a square.

The process of cutting a die horizontally results in a specific geometric shape. This can be understood as follows:

• The die is a three-dimensional shape, known as a cube.
• When a horizontal cut is made through the cube, the intersection creates a flat surface.
• This flat surface is always a square because all sides of the die are equal.
• Thus, the cross-section obtained from a horizontal cut of a die is a square.

The shadow of a solid object on a screen takes on a specific shape based on the object's form. In this case:

• The object in question is a sphere.
• When light is cast upon a sphere, the resulting shadow is typically a circle.
• This occurs because the shadow represents a 2-D projection of the sphere's 3-D shape.

Therefore, the shape of the shadow is a circle.

The shadow of the object suggests that it is a cuboidal shape.

• A book typically has a rectangular shadow, aligning with the given image.
• A ball would cast a circular shadow, which does not match.
• A die may also cast a cubic shadow, but it would likely be more complex than a simple rectangle.
• A pipe generally produces a cylindrical shadow, which is not rectangular.

Therefore, the most plausible object that corresponds to the shadow is a book, given its cuboidal form and resultant rectangular shadow.

The pipe is cylindrical whose shadow is circular (front view).