Representing 3-D in 2-D — Important Questions
ICSE · Class 8 · Mathematics
97 important questions from Representing 3-D in 2-D for ICSE Class 8 Mathematics, with answers. Part of the ICSE Class 8 Mathematics syllabus.
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Important Questions from Representing 3-D in 2-D
A polyhedron has 20 faces and 12 vertices. Find the number of edges using Euler's formula.
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30
Step 1: Use F + V - E = 2. Step 2: Put F = 20 and V = 12. Step 3: 20 + 12 - E = 2. Step 4: 32 - E = 2. Step 5: E = 30. So the number of edges is 30.
A polyhedron has 14 faces, 24 edges, and 33 vertices. Decide whether Euler's formula is satisfied.
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No, because 14 + 33 - 24 = 23
Step 1: Apply Euler's formula: F + V - E. Step 2: Substitute F = 14, V = 33, E = 24. Step 3: 14 + 33 - 24 = 47 - 24 = 23. Step 4: Since 23 is not 2, Euler's formula is not satisfied. So the correct conclusion is that this polyhedron cannot exist.
A tetrahedron has 4 faces and 4 vertices. Use Euler's formula to find the number of edges.
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6
Step 1: Use F + V - E = 2. Step 2: Put F = 4 and V = 4. Step 3: 4 + 4 - E = 2. Step 4: 8 - E = 2. Step 5: E = 6. So the number of edges is 6.
A square pyramid has 5 faces and 8 edges. Use Euler's formula to find the number of vertices.
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5
Step 1: Use F + V - E = 2. Step 2: Put F = 5 and E = 8. Step 3: 5 + V - 8 = 2. Step 4: V - 3 = 2. Step 5: V = 5. So the number of vertices is 5.
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