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Visualising Solid Shapes — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSVisualising Solid Shapes1 Mark
Question
Complete the table given below:
S. No Solid Shape of Solid Number of faces F Number of Vertices V Number of edges E F + V E + 2
$a.$ Cuboid          
$b.$ Triangular Pyramid          
$c.$ Square Pyramid          
$d.$ Rectangular Pyramid          
$e.$ Pentagonal Pyramid          
$f.$ Hexagonal Pyramid          
$g.$ Triangular Prism          
$h.$ Square Prism          
$i.$ Cube          
$j.$ Pentagonal Prism          
$k.$ Octagonal Prism          
$l.$ Heptagonal Prism          
✓

Answer

By using Euler's formula for polyhedron.
S. No Solid Shape of Solid Number of faces F Number of Vertices V Number of edges E F + V E + 2
$a.$ Cuboid $6$ $8$ $12$ $6 + 8 = 14$ $12 + 2 = 14$
$b.$ Triangular Pyramid $4$ $4$ $6$ $4 + 4 =8$ $6 + 2 = 10$
$c.$ Square Pyramid $5$ $5$ $8$ $5 + 5 = 10$ $8 + 2 = 10$
$d.$ Rectangular Pyramid $5$ $5$ $8$ $5 + 5 = 10$ $8 + 2 = 10$
$e.$ Pentagonal Pyramid $6$ $6$ $10$ $6 + 6 = 12$ $10 + 2 = 12$
$f.$ Hexagonal Pyramid $7$ $7$ $12$ $7 + 7 = 14$ $12 + 2 = 14$
$g.$ Triangular Prism $5$ $6$ $9$ $5 + 6 = 11$ $9 + 2 = 11$
$h.$ Square Prism $6$ $8$ $12$ $6 + 8 = 14$ $12 + 2 = 14$
$i.$ Cube $6$ $8$ $12$ $6 + 8 = 14$ $12 + 2 = 14$
$j.$ Pentagonal Prism $7$ $10$ $15$ $7 + 10 = 17$ $15 + 2 = 17$
$k.$ Octagonal Prism $10$ $16$ $24$ $10 + 16 = 26$ $24 + 2 = 26$
$l.$ Heptagonal Prism $9$ $14$ $21$ $9 + 14 = 23$ $21 + 2 = 23$

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