1 . Explain Polyhedron with 2 example ?
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2 .
• Explain prisms and cylinders alike ?
• How are pyramids and cones alike ?
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3. Is a square prism same as a cube ?
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4 . Using Euler’s formula find the unknown.
Refer to attachment is equation . Justify your answer .
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Class 8
Mathematics
Visualing Solid Shapes .
Answers
1. Explain Polyhedron with 2 examples .
Answer :-
A polyhedron is a 3-D figure made by joining 6 or more polygons . A polyhedron have flat faces , straight edges and pointing corners. Basically they don’t have any circular bending face/edge/vertex .
Example :-
- A Cube
→ We know that A Cube has 6 equal square faces and don’t have any circular bending face / edge / vertex .
- An Octahedron
→ It is made up of 12 identical octagons .
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2. Are Prisms and Cylinders alike ?
Answer :-
Similarities b/w them are as follows ::
→ They are solid shapes
→ Their opposite faces are congruent ( identical ) as well as parallel
→ Their base is always constant
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3. How are pyramids and cones alike ?
Answer :-
→ They are alike because their lateral surfaces always meets at a corner/vertex.
→ As we know that cones (for example – birthday cap ) have a pointing end and Pyramid ( For example – Pyramids of Egypt ) have a pointing roof where their lateral surfaces meet.
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4. Is a square prism same as a cube ?
Answer :-
Square Prism is not same as cube because a cube has all the faces same and congruent as squares but in a square prism the bases must be squares not all the faces .
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5. In this question we need to find the missing values by using the Euler’s formula
According to the Euler’s formula
F + V = E + 2
Where ,
- F is the no. of faces
- V is the no. of vertices
- E is the no. of edges
i ) F = ?
V = 6
E = 12
By applying the formula !
F + 6 = 12 + 2
F + 6 = 14
F = 14 – 6
F = 8
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ii ) F = 5
V = ?
E = 9
By applying the formula !
5 + V = 9 + 2
5 + V = 11
V = 11 – 5
V = 6
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iii ) F = 20
V = 12
E = ?
By applying the formula !
20 + 12 = E + 2
32 = E + 2
E = 32 – 2
E = 30