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Published on: 17/10/2019
Visualising Solid Shapes
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Questions + Answers key
Take MCQ Mathematics Test
1.
A solid has 20 faces and double edges to its faces. Find the number of vertices.
2.
The actual width of a store room is 320 cm. If the scale chosen to make its drawing is 1:4, then find the width of the room in the drawing.
3.
A solid has 40 faces and sixty edges. Find the number of vertices.
4.
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
5.
Use isometric dot paper, to sketch a rectangular prism with length 4 units, height 2 units and width 3 units
6.
In a town, an ice-cream parlour has displayed an ice-cream sculpture of height 360 cm. The parlour claims that these ice-creams and the sculpture are in the ratio 1 : 30. What is the height of the ice-cream served?
7.
Name the following polyhedrons and verify the Euler's formula for each of them.
8.
Using Euler's formula, find the value of unknown x, y, z, p, q and r in the following parts.
| Faces | Vertices | Edges | |
| (i) | 7 | 10 | x |
| (ii) | y | 12 | 18 |
| (iii) | 9 | z | 16 |
| (iv) | p | 6 | 12 |
| (v) | 6 | q | 12 |
| (vi) | 8 | 11 | r |
9.
Using Euler’s formula find the unknown
| Faces | ? | 5 | 20 |
| Vertices | 6 | ? | 12 |
| Edges | 12 | 9 | ? |
10.
Look at the given map of a city.
Answer the following questions:
(a) Colour the map as follows: Blue-water, Red-fire station, Orange-library, Yellow-school, Green-park, Pink-college, Purple-hospital, Brown- cemetery.
(b) Mark a green 'X' at the intersection of road 'C' and Nehru Road, Green 'V' at the intersection of Gandhi Road and road 'A'.
(c) In red, draw a short street route from library to the bus depot.
(d) Which is further East, the city park or the market?
(e) Which is further South, the primary school or the Sr. Secondary School?
1.
22
2.
80 cm
3.
22
4.
30
5.
6.
To sketch a rectangular prism of given dimensions, follow the steps given below:
Step I Draw a parallelogram with sides 4 units and 3 units. This is top of the prism.
Step II Start at one vertex. Draw a line passing through two dots. Repeat for other three vertices. Draw the hidden edges as dashed line
Step III Connect the ends of the lines to complete the prism.
7.
| S.N. | Polyhedron | F | V | F+V | E | F+V-E |
| (a) | Tetrahedron | 4 | 4 | 8 | 6 | 2 |
| (b) | Cube | 6 | 8 | 14 | 12 | 2 |
| (c) | Pentagonal prism | 7 | 10 | 17 | 15 | 2 |
8.
(i) 15 (ii) 8 (iii) 9 (iv) 8 (v) 8 (vi) 17
9.
(i) Here, F = ?,V = 6, E = 12
By Euler's formula, we have
F + V-E = 2
On putting the values of V and E, we get
F + 6 - 12 = 2 ⇒ F - 6 = 2 ⇒ F = 2 + 6 = 8
Hence, the number of faces is 8.
(ii) Here, F = 5, V =?,E = 9
By Euler's formula, we have
F + V - E = 2
On putting the values of F and E, we get
5 + V - 9 = 2 ⇒ V - 4 = 2
⇒ V = 2 + 4 ⇒ V = 6
Hence, the number of vertices is 6.
(iii) Here, F = 20, V = 12, E =?
By Euler's formula, we have
F + V - E = 2
On putting the values of F and V, we get
20 + 12 - E = 2 ⇒ 32 - E = 2
⇒ 32 - 2 = E ⇒ E =30
Hence, number of edges is 30.
10.
(a) The shaded (coloured) map according to the question is as follows:
(b) Intersection of road C and Nehru road is marked by X and intersection of Gandhi road and road A is marked by Yin map given in (a) part.
(c) Short street route from library to the bus depot is Library ⟶ Nehru road ⟶ Road C ⟶ Bus depot.
(d) City Park is in the East.
(e) Sr. Secondary School is in the South.
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CBSE 8th Standard CBSE Subjects
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