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Class 8 Exploring Some Geometric Themes worksheet
CBSE Mathematics. Faces, vertices and edges, Euler's formula, prisms and pyramids, nets, painted cubes, Sierpinski and Koch fractals. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
A solid has 8 faces and 12 vertices. By Euler's formula, how many edges does it have?
- 22
- 20
- 19
- 18
Answer
(d) 18
F + V − E = 2: 8 + 12 − 2 = 18
- 2.
A design starts with 5 shaded triangles. Each step of the Sierpinski pattern replaces every shaded triangle with 3 smaller ones. After 5 steps, how many shaded triangles are there?
- 1215
- 75
- 5120
- 1220
Answer
(a) 1215
5 × 3⁵
- 3.
Euler's formula for a solid with flat faces is:
- F − V − E = 0
- F + V + E = 2
- F + V − E = 2
- F + E − V = 2
Answer
(c) F + V − E = 2
faces, vertices, edges
Section B · short answer
- 4.
For a prism with a heptagonal base, find the number of faces, vertices and edges, and check Euler's formula.
Answer
F = 9, V = 14, E = 21; 9 + 14 − 21 = 2
faces 7 + 2, vertices 2 × 7, edges 3 × 7
- 5.
For a pyramid with a decagonal base, find the number of faces, vertices and edges, and check Euler's formula.
Answer
F = 11, V = 11, E = 20; 11 + 11 − 20 = 2
faces 10 + 1, vertices 10 + 1, edges 2 × 10
Section C · long answer
- 6.
Ananya paints a big wooden cube and cuts it into 216 equal small cubes (6 along each edge). How many small cubes have no paint at all? How many have paint on exactly two faces?
Answer
64 with no paint; 48 with two faces
inside cube 4³; 12 edges × 4
Fresh sheets for your child
In the app, every Exploring Some Geometric Themes sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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