Explore repeating patterns and three-dimensional shapes with these MCQs for Class 8 Maths, Ganita Prakash Part 2, Chapter 4: Exploring Some Geometric Themes. Each question includes an answer and explanation. The sets cover Sierpinski patterns, the Koch Snowflake, cut-out shapes, prisms, pyramids, nets and projections. Small sketches can help you follow how the patterns grow and how solids unfold or appear from different viewpoints.
Class 8 Maths Ganita Prakash Part 2 Chapter 4 MCQs with Answers
Set 1: Self-Similarity and Sierpinski Patterns MCQs (Questions 1–5)
Q1. Which feature makes a geometric pattern self-similar?
[A]. It always has exactly four sides
[B]. Every part has exactly the same size
[C]. The same or a similar pattern appears at smaller and smaller scales
[D]. It has only straight edges
Q2. In the Sierpinski Carpet construction, Step 0 is one square. At each step, every remaining square is replaced by 8 smaller squares. How many small squares remain at Step 3?
[A]. 512
[B]. 64
[C]. 24
[D]. 729
Q3. A Sierpinski Carpet starts with no holes at Step 0. The numbers of new holes made at Steps 1, 2, and 3 are 1, 8, and 64. How many holes are present in total at Step 3?
[A]. 512
[B]. 72
[C]. 64
[D]. 73
Q4. The starting square of a Sierpinski Carpet has area 1 square unit. Each step removes the middle one of 9 equal squares from every remaining square. What area remains after Step 2?
[A]. 7/9 square unit
[B]. 8/9 square unit
[C]. 1/81 square unit
[D]. 64/81 square unit
Q5. In a Sierpinski Triangle, Step 0 is one equilateral triangle. At each step, every remaining triangle is replaced by 3 smaller triangles. How many small triangles remain at Step 3?
[A]. 9
[B]. 64
[C]. 12
[D]. 27
Set 2: Fractal Patterns and Shape Transformations MCQs (Questions 6–10)
Q6. A Sierpinski Triangle starts without holes. At each step, one central triangle is removed from each triangle remaining after the previous step. What is the total number of holes at Step 3?
[A]. 27
[B]. 3
[C]. 9
[D]. 13
Q7. The starting triangle of a Sierpinski Triangle has area 1 square unit. Each step removes the central one of 4 equal triangles from every remaining triangle. What area remains after Step 2?
[A]. 1/16 square unit
[B]. 1/2 square unit
[C]. 3/4 square unit
[D]. 9/16 square unit
Q8. A Koch Snowflake starts with an equilateral triangle at Step 0. At each step, every side is replaced by 4 smaller line segments. How many sides does the boundary have at Step 2?
[A]. 12
[B]. 16
[C]. 48
[D]. 9
Q9. A Koch Snowflake starts with an equilateral triangle of side 1 unit. Each step replaces a side by 4 segments, each one-third as long. What is the perimeter at Step 2?
[A]. 4 units
[B]. 3 units
[C]. 16/3 units
[D]. 16/9 units
Q10. Each corner of a square is cut off by a straight cut joining the midpoints of its two adjacent sides. What shape remains in the centre?
[A]. A regular hexagon
[B]. An equilateral triangle
[C]. A square
[D]. A regular pentagon
Set 3: Cut-Out Shapes, Solid Views and Prisms MCQs (Questions 11–15)
Q11. Each side of an equilateral triangle is divided into three equal parts. Each corner is cut off by joining the two nearest division marks. What shape remains?
[A]. A regular pentagon
[B]. A regular hexagon
[C]. A square
[D]. An equilateral triangle
Q12. A right circular cylinder stands upright on its circular base. What are the outlines of its top view and front view, respectively?
[A]. Circle and triangle
[B]. Triangle and circle
[C]. Rectangle and triangle
[D]. Circle and rectangle
Q13. How many faces, edges, and vertices does a cube have, in that order?
[A]. 12, 6, 8
[B]. 6, 12, 8
[C]. 6, 8, 12
[D]. 8, 12, 6
Q14. A prism has two congruent 10-sided polygons as its opposite faces. How many faces, edges, and vertices does it have, in that order?
[A]. 12, 20, 30
[B]. 10, 20, 10
[C]. 12, 30, 20
[D]. 11, 20, 11
Q15. A prism has two congruent n-sided polygons as its opposite faces. Which expression gives its total number of faces?
[A]. 3n
[B]. n + 2
[C]. 2n
[D]. n + 1
Set 4: Pyramids and Nets of Solids MCQs (Questions 16–20)
Q16. A pyramid has a 10-sided polygon as its base. How many faces, edges, and vertices does it have, in that order?
[A]. 10, 20, 10
[B]. 11, 20, 11
[C]. 12, 30, 20
[D]. 11, 10, 20
Q17. Which description fits a regular tetrahedron?
[A]. A solid with four equilateral triangular faces
[B]. A solid with six square faces
[C]. A solid with one square and four triangular faces
[D]. A solid with two triangular and three rectangular faces
Q18. How many different net structures can a cube have when rotated or flipped copies of a net are counted as the same structure?
[A]. 11
[B]. 6
[C]. 8
[D]. 12
Q19. A closed right circular cylinder is cut along its height and unfolded. Which pieces form its net?
[A]. One sector of a circle and one circle
[B]. One rectangle and two congruent circles
[C]. One triangle and two circles
[D]. Two rectangles and one circle
Q20. The curved surface of a right circular cone is slit along a straight line from its vertex to its base and unrolled. What flat shape does it form?
[A]. A rectangle
[B]. A sector of a circle
[C]. An equilateral triangle
[D]. A complete circle
Set 5: Solids, Surface Paths and Projections MCQs (Questions 21–25)
Q21. Two identical square pyramids are joined at their square bases to form an octahedron. How many triangular faces are on the outside of the new solid?
[A]. 8
[B]. 6
[C]. 10
[D]. 12
Q22. An ant’s starting point and destination are marked on a cuboid net. The straight line joining them passes outside the net. What does this mean for that line?
[A]. It represents a path through the cuboid’s interior
[B]. Its length must be zero
[C]. It does not represent a continuous path along that unfolded surface
[D]. It must be the shortest surface path
Q23. On an unfolded cuboid, a valid straight path forms the hypotenuse of a right triangle whose perpendicular sides are 24 cm and 32 cm. What is the path length?
[A]. 56 cm
[B]. 40 cm
[C]. 8 cm
[D]. 1,600 cm
Q24. Why may several different unfoldings need to be compared when finding the shortest path between two points on a cuboid’s surface?
[A]. Different unfoldings can give valid straight paths of different lengths
[B]. A surface path can never become straight on a net
[C]. Unfolding changes the lengths of the edges
[D]. Every net gives exactly the same straight-line distance
Q25. A line segment of length l is projected perpendicularly onto a plane. If its projected length is p, which relation is always true?
[A]. p = 2l
[B]. p > l
[C]. p < 0
[D]. 0 ≤ p ≤ l
Set 6: Views, Projections and Isometric Drawings MCQs (Questions 26–30)
Q26. An object’s projection onto the horizontal plane below it is called its:
[A]. Front view
[B]. Net
[C]. Top view
[D]. Side view
Q27. Two cuboids have equal heights and equal widths but different depths. Their front faces are parallel to the front-view plane. Which statement is correct?
[A]. Their front views can be identical despite their different depths
[B]. Their front views can be identical despite their different depths
[C]. Their front views must have different heights
[D]. Their front views must show their complete depths
Q28. A flat parallelogram is projected perpendicularly onto a plane so that its projection still has four sides. Which statement must be true?
[A]. Its projection has two pairs of parallel opposite sides
[B]. All four projected sides must be equal
[C]. Its projection must be a square
[D]. All its projected angles must be right angles
Q29. A cube is oriented for an isometric projection, so all its projected edges have equal length. What shape is the outer boundary of its projection?
[A]. A regular hexagon
[B]. An equilateral triangle
[C]. A square
[D]. A regular pentagon
Q30. Four unit cubes are joined face-to-face in one straight row along the height axis of an isometric drawing. What are the solid’s length, depth, and height, respectively?
[A]. 1 unit, 4 units, 1 unit
[B]. 4 units, 4 units, 4 units
[C]. 1 unit, 1 unit, 4 units
[D]. 4 units, 1 unit, 1 unit
Revise Patterns, Nets and Views with Sketches
When revising fractals, distinguish the number of new holes from the total number of holes and track the area or perimeter factor at each step. For solids, label faces, edges and vertices on a sketch. Before comparing surface paths, confirm that each path stays within its net, then revisit the projection questions from different viewpoints.
