Exercise 23B
Question 1
1. Look at the figure and answer the following questions.
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(i) Name the 8 vertices.
(iii) Name the 6 faces.
(ii) Name the 12 edges.
(iv) The length of some of the edges are marked by the letters x , y and z. Indicate the lengths of all the other edges.
(v) If $A B C D$ be called the base, then name the four side faces.
(vi) If $A B C D$ be the base, name a line segment which represents the height of the cuboid.
(vii) Name the
(a) face opposite to $A E H D$, (b) face adjacent to BCGF
(c) faces which meet in the edge $A B$,
(d) three edges which meet in the vertex $H$.
(viii) (a) Name the three faces which have vertex $A$ in common.
(b) Also, name the vertex, in which the other three faces meet.
Question 2
| Column I | Column II | |
| (i) | One curved surface , one plane surface | (a) Cube |
| (ii) | One unbroken curved surface | (b) Cylinder |
| (iii) | One curved surface, two plane faces of equal size | (c) Triangular Prism |
| (iv) | Six square faces | (d) Sphere |
| (v) | One square base, four triangular faces | (e) Cone |
| (vi) | Three rectangular faces, two triangular base of equal size | (f) Pyramid |
Question 3
Name the solid(s) that have
(i) 4 faces
(ii) 5 faces
(iii) 6 faces
(iv) 1 surface
(v) 4 vertices
(vi) 5 vertices
(vii) 6 vertices
(viii) no vertices
(ix) 9 edges
(x) 2 edges
(xi) 1 edge
(xii) no edges
(xiii) 5 faces and 5 vertices
Question 4
Complete the following table and verify the Euler's formula
| Name of Solids | Number of Faces (F) | Number of Vertices (V) | Number of Edges (E) | Eulers Formula (F+V-E) | |
| (i) | Cube | ||||
| (ii) | Rectangular prism | ||||
| (iii) | Triangular prism | ||||
| (iv) | Square pyramid | ||||
| (v) | Rectangular pyramid | ||||
| (vi) | Triangular pyramid |
Question 5
5. For each solid, count the number of faces, vertices and edges. Check that Euler's formula is true for each one.
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Multiple Choice Questions (MCQs)
Tick (✔) the correct option.
6. A gift box is in the shape of a pentagonal prism. How many faces, edges and vertices does the box have?
(a) 6 faces, 10 edges, 6 vertices
(b) 7 faces, 12 edges, 10 vertices
(c) 7 faces, 15 edges, 10 vertices
(d) 8 faces, 18 edges, 12 vertices
7. Which two solids have the same number of vertices?
(a) rectangular prism and rectangular pyramid
(b) triangular prism and rectangular pyramid
(c) rectangular prism and pentagonal pyramid
(d) triangular prism and pentagonal pyramid
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