Exploring Some Geometric Themes — Class 8 MCQs with Answers

Exploring Some Geometric Themes — important questions & MCQs with answers (Class 8 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

   A fractal is a shape that:

   Ahas no pattern at allBrepeats a similar pattern at smaller and smaller scalesCis always a circleDhas only straight edges
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   Answer: repeats a similar pattern at smaller and smaller scales

   Explanation: A fractal is built by repeating the same pattern at ever-smaller scales, not something with no pattern, always a circle, or only straight edges.

2. Q2 of 6Easy

   The net of a solid is:

   Athe shadow of the solidBa flat shape that folds up into the solidCa solid made of netsDhalf the solid
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   Answer: a flat shape that folds up into the solid

   Explanation: A net is the flat, 2-D pattern that folds up along its edges to form the 3-D solid — not a shadow, a solid made of nets, or just half the solid.

3. Q3 of 6Medium

   A triangular prism has how many faces?

   A6B5C4D9
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   Answer: 5

   Explanation: A triangular prism has 2 triangular ends and 3 rectangular side faces: 2 + 3 = 5 faces in total, not 6 or 4.

4. Q4 of 6Medium

   An upright cylinder has a front view shaped like a:

   AcircleBtriangleCsquareDrectangle
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   Answer: rectangle

   Explanation: Seen from the side, an upright cylinder's straight sides and flat top and bottom outline a rectangle, not a circle, triangle, or square.

5. Q5 of 6Hard

   A shape is scaled up so every length is doubled. Its area increases by a factor of:

   A2B8C6D4
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   Answer: 4

   Explanation: Area scales by the square of the length factor: doubling every length multiplies area by 2² = 4, not 2, 6, or 8.

6. Q6 of 6Hard

   A cuboid measures 3 × 4 × 5 units. The number of unit cubes it contains is:

   A12B60C47D20
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   Answer: 60

   Explanation: The number of unit cubes filling a cuboid equals its volume: 3 × 4 × 5 = 60, not the sum 3 + 4 + 5 = 12 or any other combination.

Exploring Some Geometric Themes notes: key concepts (Class 8 Mathematics)

This chapter explores two geometric themes. Fractals are self-similar shapes — like the fern, the Koch snowflake and the Sierpiński triangle — that repeat a pattern at smaller and smaller scales, which also shows how areas and volumes grow when a shape is scaled. Visualising solids covers nets that fold into cubes, cuboids, prisms and pyramids, counting their faces, edges and vertices (with Euler's relation F + V − E = 2 as a check), and the front, top and side views of a solid.

Fractal

A shape that repeats the same or a similar pattern over and over at smaller and smaller scales, such as a fern, the Koch snowflake or the Sierpiński triangle.

Self-similarity

The defining feature of a fractal: any small part of it looks like the whole shape, so zooming in reveals smaller copies of the same pattern.

Scaling and dimension

When a shape is scaled so each length is multiplied by k, its area is multiplied by k² and its volume by k³ — a tripled side gives 9× the area and 27× the volume.

Solid

A three-dimensional shape such as a cube, cuboid, prism, pyramid, cylinder, cone or sphere, bounded by faces, edges and vertices.

Net of a solid

A flat pattern that folds up to form the solid, with no overlaps or gaps — a cube's net is six squares, a cylinder's is two circles and a rectangle.

Faces, edges and vertices

A face is a flat surface, an edge is where two faces meet, and a vertex is a corner. A cube has 6 faces, 12 edges and 8 vertices.

Euler's relation

For a simple polyhedron, faces + vertices − edges = 2 (F + V − E = 2), which lets you find a missing count from the other two.

Prisms and pyramids

A prism has two identical end-faces joined by rectangles; a pyramid has one base and triangular faces meeting at an apex. An n-gonal prism has n + 2 faces, 2n vertices and 3n edges.

Views of a solid

The outlines seen from the front, top and side. A cylinder is a rectangle from the front but a circle from the top, while a cube is a square from all three.

Profiles from a viewpoint

The same solid can have very different outlines from different directions — a cone is a triangle head-on and a circle from above.