Representing 3-D in 2-D — Flashcards
ICSE · Class 8 · Mathematics
26 flashcards for Representing 3-D in 2-D (ICSE Class 8 Mathematics) to test yourself on key terms and facts. Sample: "A solid has 5 faces, 5 vertices.
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A solid has 5 faces, 5 vertices, and 8 edges. Check whether Euler's Formula is satisfied.
Answer
Step 1: Use Euler's Formula: F + V - E = 2 Step 2: Substitute the values: 5 + 5 - 8 Step 3: Calculate: 10 - 8 = 2 Answer: Euler's Formula is satisfied.
Find the number of vertices if a polyhedron has 8 faces and 12 edges.
Answer
Step 1: Use Euler's Formula: F + V - E = 2 Step 2: Substitute F = 8 and E = 12 8 + V - 12 = 2 Step 3: Simplify: V - 4 = 2 Step 4: Add 4 to both sides: V = 6 Answer: 6 vertices.
Find the number of faces if a polyhedron has 6 vertices and 9 edges.
Answer
Step 1: Use Euler's Formula: F + V - E = 2 Step 2: Substitute V = 6 and E = 9 F + 6 - 9 = 2 Step 3: Simplify: F - 3 = 2 Step 4: Add 3 to both sides: F = 5 Answer: 5 faces.
Find the number of edges if a polyhedron has 20 faces and 12 vertices.
Answer
Step 1: Use Euler's Formula: F + V - E = 2 Step 2: Substitute F = 20 and V = 12 20 + 12 - E = 2 Step 3: Simplify: 32 - E = 2 Step 4: Subtract 2 from 32: E = 30 Answer: 30 edges.
Can a polyhedron have 14 faces, 24 edges, and 33 vertices?
Answer
Step 1: Use Euler's Formula: F + V - E = 2 Step 2: Substitute the values: 14 + 33 - 24 Step 3: Calculate: 47 - 24 = 23 Step 4: Compare with 2 23 is not equal to 2 Answer: No, it cannot.
A tetrahedron has how many faces, vertices, and edges?
Answer
A tetrahedron is a pyramid with triangular base. Step 1: Count its faces = 4 Step 2: Count its vertices = 4 Step 3: Count its edges = 6 Check: 4 + 4 - 6 = 2 Answer: 4 faces, 4 vertices, 6 edges.
A cube has how many faces, vertices, and edges? Verify using Euler's Formula.
Answer
Step 1: A cube has 6 faces, 8 vertices, and 12 edges Step 2: Apply Euler's Formula 6 + 8 - 12 = 2 Step 3: The result is 2 Answer: 6 faces, 8 vertices, 12 edges.
A triangular prism has 5 faces, 6 vertices, and 9 edges. Check Euler's Formula.
Answer
Step 1: Use Euler's Formula: F + V - E = 2 Step 2: Substitute values: 5 + 6 - 9 Step 3: Calculate: 11 - 9 = 2 Answer: The formula is satisfied.
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