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Maths 3 Marks Question

Visualising Solid Shapes · Jharkhand Board (JAC) STD 8 (Jharkhand - English Medium). 5 questions.

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3 Marks Question

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5 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
Draw a map of your school playground. Mark all necessary places like $2$ library, Playground, Medical Room, Classrooms, Assembly area, etc.
Answer
A number of maps can be drawn for a school from which one map is given below:
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Question 23 Marks
Draw a prism with its base as regular hexagon with one of its face facing you. Now draw the top view, front view and side view of this solid.
Answer
The following figure shows a prism with its base as regular hexagon with one of its face to us. And also, we shows the top view, front view and side view of the prism.
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Question 33 Marks
Use a ruler to measure the distance in $cm$ between the places joined by dotted lines. If the map has been drawn using the scale $1\ cm : 10\ km$, find the actual distances between
$1.$ School and Library
$2.$ College and Complex
$3.$ House and School
Answer
Given scale is $1 \ cm: 10 \ km$, i.e. $1 \ cm$ in a picture $=10 \ km$ of actual distance:
$1.$ The distance between the school and libarary in the picture $=6 \ cm$.
Hence, the actual distance between the school and library $=6 \times 10=60 \ km$.
$2.$ Distance between the college and complex in the picture $=2 \ cm$.
Hence, the actual distance between the college apd complex $=2 \times 10=20 \ km$.
$3.$ Distance between the house and school in the picture $=3.5 \ cm$.
Hence, the actual distance between the house and school $=3.5 \times 10=35 \ km$.
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Question 43 Marks
Can a polyhedron have $V = F = 9$ and $E = 16$? If yes, draw its figure.
Answer
Given, vetices $= 9$, faces $= 9$ and edges $= 16$Using Euler's formula for polyhedron,$ F + V - E = 2$
[where, $F =$ faces, $V =$ vertices and $E =$ edges]
$\Rightarrow 9 + 9 -16 = 2$
$\Rightarrow 18 - 16 = 2$
$\Rightarrow 2 = 2$
Hence, the given values satisfies the Euler's formula. So, a polyhedron can have $V = F = 9$ and $E = 16$
Thus, we can draw a octagonal pyramid.
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Question 53 Marks
Complete the table given below by putting tick mark across the respective property found in the solids mentioned.Solids
Properties Cone Cylinder Prism Pyramid
1. The figure is a Polyhedron.        
2. The figure has diagonals.        
3. The shape has curved edges.        
4. The base of figure is a polygon.        
5. The bases are congruent.        
6. The base of figure is a polygon and other faces meet at a single point.        
7. The base of figure is a curved edge and other faces meet at a single point.        
Answer
On the basis of properties and features of cone, cylinder, prism and pyramid, we can fill the given table as follows:Solids
Properties Cone Cylinder Prism Pyramid
1. The figure is a Polyhedron. $\times$ $\times$ $\checkmark$ $\checkmark$
2. The figure has diagonals. $\times$ $\times$ $\times$ $\checkmark$
3. The shape has curved edges. $\checkmark$ $\checkmark$ $\times$ $\times$
4. The base of figure is a polygon. $\times$ $\times$ $\checkmark$ $\checkmark$
5. The bases are congruent. $\times $ $\checkmark$ $\checkmark$ $\times $
6. The base of figure is a polygon and other faces meet at a single point. $\times$ $\times$ $\times$ $\checkmark$
7. The base of figure is a curved edge and other faces meet at a single point. $\checkmark$ $\times $ $\times$ $\times $
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