Unit Test (Solutions): Shapes Around Us | Mathematics for Class 4 (Maths Mela: New NCERT) PDF Download

Total Marks: 20
Attempt all questions.

• Question numbers 1 to 4 carry 1 mark each.
• Question numbers 5 to 9 carry 2 marks each.
• Question numbers 10 to 11 carry 3 marks each.

Q1. A shape with 6 faces, 12 edges, and 8 corners is called: (1 Mark)
(a) Cube
(b) Triangular Prism
(c) Square Pyramid
(d) Sphere
Ans:  (a) Cube

A cube has 6 faces, 12 edges, and 8 corners, as each face is a square, and it has 8 vertices and 12 edges connecting them.

Q2. How many flat faces does a triangular pyramid have? (1 Mark)
(a) 3
(b) 4
(c) 5
(d) 6
Ans:  (b) 4

A triangular pyramid (tetrahedron) has 4 flat faces, all of which are triangles.

Q3. The length of the diameter of a circle is: (1 Mark)
(a) Half the radius
(b) Equal to the radius
(c) Double the radius
(d) Three times the radius
Ans: (c) Double the radius

The diameter of a circle is twice the length of the radius, as it is the line from one side of the circle to the other through the center. 

Q4. A shape with one curved face, one flat face, and one edge is: (1 Mark)
(a) Sphere
(b) Cylinder
(c) Cone
(d) Cube
Ans: (c) Cone

A cone has one curved face, one flat circular base, and one edge where the curved surface meets the base.

Q5. A cuboid has 6 faces. How many edges and corners does it have? (2 Mark)
Ans: Edges: 12, Corners: 8

A cuboid has 6 rectangular faces, 12 edges (4 along length, 4 along width, 4 along height), and 8 corners (vertices where edges meet).

Q6. A shape has 5 faces, 6 corners, and 9 edges, with 2 faces being triangles. Name the shape and calculate F + V - E. (2 Mark)
Ans: Shape: Triangular Prism, F + V - E = 2

A triangular prism has 5 faces (2 triangular, 3 rectangular), 6 corners, and 9 edges. Calculate: F (5) + V (6) - E (9) = 5 + 6 - 9 = 2.

Q7. A circle is folded in half twice. If the radius is 5 cm, what is the length of the crease formed each time? Explain your answer. (2 Mark)
Ans: Length of crease: 10 cm

Folding a circle in half creates a crease that is the diameter, which is twice the radius. For a radius of 5 cm, the diameter is 2 × 5 = 10 cm. Folding twice in different ways still results in a diameter crease, so the length is 10 cm each time.

Q8. A die has the face numbered 1 opposite to the face numbered 6. If the face numbered 2 has common edges with faces numbered 3, 4, 5, and 6, which face has no common edge with the face numbered 2? (2 Mark)
Ans: Face numbered 1

In a die, opposite faces do not share edges. Since face 1 is opposite face 6, and face 2 shares edges with faces 3, 4, 5, and 6, face 1 has no common edge with face 2.

Q9.  Write True or False: (2 Mark)
(i) A cone has 2 edges. 
(ii) A sphere has no faces or corners. 
(iii) All corners in a rectangle are right angles. 
(iv) A cuboid and a cube both have 12 edges and 8 vertices.

Ans: 
(i) False, A cone has only 1 edge, where the curved surface meets the circular base.
(ii) True 
(iii) True
(iv) True

Q10. Fill the table for the following shapes:  (3 Mark)
Cuboid, Triangular Pyramid, Rectangular Prism. Include the number of faces (F), corners (V), and edges (E). Calculate F + V - E for each shape. What do you notice about the result?
Ans:

• ​Cuboid: 6 faces (rectangles), 8 corners, 12 edges. F + V - E = 6 + 8 - 12 = 2.
• Triangular Pyramid: 4 faces (triangles), 4 corners, 6 edges. F + V - E = 4 + 4 - 6 = 2.
• Rectangular Prism: Same as cuboid, 6 faces, 8 corners, 12 edges. F + V - E = 6 + 8 - 12 = 2.
• Observation: For all shapes, F + V - E = 2, indicating Euler’s formula for polyhedra. 

Q11. A shape has 4 right angles and 4 sides. Name the shape and identify the number and types of angles (acute, right, or obtuse) if one side is pushed to form a new four-sided shape. Explain how the angles in the new shape differ from the original.  (3 Mark)
Ans: Original Shape: Rectangle
Angles in Original Shape: 4 right angles (90° each).
New Shape (e.g., Parallelogram): When one side of a rectangle is pushed, it forms a parallelogram. The new shape has 2 acute angles and 2 obtuse angles, with no right angles.