Visualising Solid Shapes - Class 7 Maths - Extra Questions

The net of a rectangular prism has _______ rectangles. (Hint: Every square is a rectangle but every rectangle is not a square.)

Rectangular prism has two rectangles at opposite ends and $$4$$ rectangles on each side connecting end rectangles.
So, in total has $$6$$ rectangles.


Draw the net of a regular tetrahedron with side 6 cm.

The net of a regular tetrahedron with side 6 cm each is shown below:
1653562_1793077_ans_7b985753246641df920884256e4267c6.png


If you look at this object from the top, what will you see?

477205.PNG

We will see the top view as

513358_477205_ans.PNG



Dice are cubes with dots on each face. Opposite faces of a die always have a total of seven dots on them.
Here are two nets to make dice(cubes); the numbers inserted in each square indicate the number of dots in that box.
Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to $$7$$.

1646891_0932a8b00ce04ab8bbe87dfb4ed383cc.png

$$\textbf{Explanation}$$
$$\textbf{First Net :}$$
Since, the number left to $$4$$ will be opposite to $$5$$, it should be $$2.$$
The number left to $$2$$, will be opposite to $$4$$, it will be $$3. 1$$ will be put in leftover face, which will come to opposite of $$6.$$
$$\textbf{Second Net :}$$
When folded, $$6$$ comes opposite to $$1, 4$$ comes opposite to $$3,$$ and $$5$$ comes opposite to $$2.$$

2136876_1646891_ans_393f1e0fb7be46aa91c62690cccf258b.JPG


Define the following terms :
Discrete frequency distribution

A frequency distribution is a table of observed values in a sample, with the number if time each value was observed.
A discrete frequency distribution lists all the observed values rather listing the ranges.
For example: You may use discrete frequency distribution to count the integers.
Or you can use it to record the number of children in a sample of families, how many has one child or zero children and so on.


Draw the net of the following cuboid:
1793083_fc8d693fa3a64557be0c8c115b73dfd5.png

The net of the given cuboid is shown below:
1653571_1793083_ans_f96c111cbe8742708c08e4f703c75416.png


Draw the net of the following solid.
1793100_9470357bb1884701b514042398c2805a.png

The net of the given solid is shown below:
1653681_1793100_ans_d6aedbf69c4e43099d67623f912c4980.png


Use isometric dot paper to draw a tetrahedron


1653724_1793145_ans_bd13e214c3ee4aa2aa3283c7214e2d19.png


Draw the net of a regular hexahedron with side 3 cm. (Hint: Regular hexahedron - cube)

The net of a regular hexahedron with side 3 cm each is shown below:
1653554_1793073_ans_16946780404948b79d41fe2b73140e7a.png


Use isometric dot paper to draw a square prism with side of 2 units


1653729_1793148_ans_1954f8533807445e924bd77c3ffaad66.png


Identify if the net in the figure can be used to form a cube:


1823465_2861853119654403bc3792e7d5eb105d.png

In the given figure, the net cannot be folded into a cube by folding the six faces of the net 
Therefore, it is not a cube net.




Complete the table given below by putting tick mark across the respective property found in the solids mentioned.

                                                          Solids
 PropertiesCone Cylinder Prism Pyramid 
 The figure is a polyhedron.    
 The figure has diagonals.    
 The shape has curved edges    
 The base of figure is a polygon    
 The bases are congruent    
 The base of figure is a polygon and other faces meet at a single point    
 The base of figure is a curved edge and other faces meet at a single point    


1653670_1793090_ans_89b0594c36fb4dc2b97a74f16326fd35.png


Draw the net of the following shape.
1793098_c10b28ce93a04d9e8833543e74673f76.png

The net of the given shape is shown below:
1653677_1793098_ans_a3fa5d5007e045b4aef9f470527f4b02.png


Two cubes, each with $$3 cm$$ edge, are placed side by side to form a cuboid. For this cuboid, draw an isometric sketch

An isometric sketch of a cuboid is shown in the figure



1748998_1823519_ans_d8c6dc5715d34e3ba01d012bdbed3565.png


Two cubes, each with $$3 cm$$ edge, are placed side by side to form a cuboid. For this cuboid, draw an oblique sketch

An oblique sketch of a cuboid is shown in the figure

1748995_1823515_ans_dbc166d5accb4182a1c09f4b4d9dc00f.png


Draw front view of the diagram.

477207.PNG

The front view of the diagram is

513379_477207_ans.PNG


Sketch top, front and side view for the following diagram.

477206.PNG

The top, front and side views are

513364_477206_ans_ce1957c1a604429099e8e66890e9c424.png


Identify if the net in the figure can be used to form a cube:


1823481_517061f93a7d4999bc33d7d872a54eb3.png

In the given figure, the net can be folded into a cube when its faces are folded one over the other
Therefore, it is a cube net


A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions).

703927_504cff85d3764a618d89de952080e976.png

When an object is placed in the path of a ray of light, the object casts a projected image on the wall that intercepts the ray of light. Please note that this projected image is a two dimension figure on the wall. So, this project image will be the two dimensional version of the object in question.

A sphere will thus have a circle as its projected image. So the ball's shadow will be a circle. Hence item "A" from List I will be matched to item "2" A Circle in the list II.

A cylinder will have a rectangle as its projected image. So, the cylinder's shadow will be a rectangle. Hence item "B" from List I will be matched to item "1" A rectangle in the list II.

A book will have a rectangle as its projected image. So, the book's shadow will be a rectangle. Hence item "C" from List I will be matched to item "3" A rectangle in the list II.


Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:
(a) A cuboid of dimensions $$5\ cm, 3\ cm$$ and $$2\ cm$$. (Is your sketch unique?)
(b) A cube with an edge $$4\ cm$$ long.

The sketch is not unique. Because, any of the three faces can be placed front and the view could be different eventhough the object is the same.
1180719_703920_ans_c613c2f1af0746a2b2ab621ba8b450f1.png


Can any  of the following be a net for a die? If no, explain your answer.
1451738_719b0742fd464d199814e6c23eaee65b.PNG

$$\textbf{Hint: We will solve this question using nets and oblique skeches}$$

$$\textbf{Step-1: For the first figure}$$
                $$\text{In this figure, opposite faces contain 4-3, 6-1.}$$
                $$\text{As their sum is 7, they can be a net for a die.}$$
$$\textbf{Step-2: For the second figure}$$
                $$\text{In this figure, opposite faces contain 1-4, 3-6.}$$
                $$\text{As their sum is not 7, the figure cannot be a net for a die.}$$

$$\textbf{Final Answer: Only}$$ $$\mathbf{(i)}$$ $$\textbf{can be a net for a die.}$$


Draw nets for each of the following polyhedrons:
1673223_84fd3e0be238478cba2ec78dcf4ab65f.png

Net for cube is shown in the above figure.
1876781_1673223_ans_8183facdc43e4ce58672cb452d5a11e2.png


Name any four objects from your environment, which have the form of a cuboid. 

The four objects from the environment which have the form of a cuboid are as follows and the pictures of the objects are shown in the above image:

1. A storage box 

2. A cupboard 

3. A book

4. A duster

1424720_1674879_ans_7f4104ce6f514843b60b504474904f3f.jpg


Give two new examples of  the following three dimensional shape:
Cuboid

Examples of cuboid are as follows: 

1. Matchbox
2. Smart phone


What is the shape of:
a sweet laddoo

Consider the picture of sweet laddoo shown in the above image:

Hence, from the image, we find that the shape of the sweet laddoo is sphere.

1424355_1674871_ans_a8daa857043b4081beddf992c860d55c.png


Out of the following four nets there are two correct nets to make a tetrahedron. Identify them.
1676689_5f964a6ff7624d5cb160543670125c86.png

$$(i), (iii)$$


What is the shape of:
a match box

Consider a match box shown in the above image:

Hence, from the image, we find that the shape of the match box is cuboid.

1424349_1674863_ans_359a84439fe34c5592c79439fd630488.png


Draw nets for each of the following polyhedrons:

1673224_31fb7446f2da4867b838b2b8ab54475f.png

Net of a triangular prism is shown in above figure.
1876780_1673224_ans_d1c24b0f9d004c1fab3a91663e29406a.png


Define the following terms :
Frequency of distribution

$$Frequency\ Distribution:-$$
A frequency distribution is an arrangement of instances in which a variable takes each of its possible values. A frequency distribution depicts a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in those classes.


What is the shape of:
a rod-roller

Consider a rod-roller shown in the above image:

Hence, from the image, we find that the shape of the rod-roller is cylinder.

1424351_1674865_ans_ccdb2f7a17aa435ba95f74e73a2675bb.png


Here is an incomplete net for making a cube. Complete it in alleast two different ways.
1676710_2fe1e158ff5345b6a338e7651efb5da6.png

For, cube we need six square faces, $$3$$ of them are given in figure.
So, adding other $$3$$ as shown in both diagrams will complete unfolded view of cube.

1681405_1676710_ans_187b11e75b394fd2946afac760cbdd1e.png


The dimensions of a cuboid are $$6\ cm,\ 4\ cm$$ and $$3\ cm.$$ Draw two different types of oblique sketches for this cuboid.

$$(i)$$ First cuboid have length equal to $$6\ cm$$, breadth equal to $$3\ cm$$ and height equal to $$4\ cm.$$

$$(ii)$$ Second cuboid have length equal to $$4\ cm$$, breadth equal to $$6\ cm$$ and height equal to $$3\ cm.$$

1748994_1823505_ans_66eae0eafa704957a31ebe362d34f327.png


Dice are cubes with dot or dots on each face. Opposite faces of a die always have a total of seven on them.
In the figure is given a net to make dice (cube), the numbers inserted in each square indicate the number of dots in it.
Insert suitable numbers in each blank so that numbers in opposite faces of the die have a total of seven dots.

1823618_9f288be8447543eeb97d24392d719a8b.png

Following is the figure where the numbers are inserted such that the numbers in opposite faces of the die have a total of seven dots

In the given cube net, $$4$$ lies opposite to $$3$$, $$6$$ lies opposite to $$1$$ and $$5$$ lies opposite to $$2$$

1747015_1823618_ans_8adde567a80f482a9000f3cbbee46275.png


Dice are cubes with dot or dots on each face. Opposite faces of a die always have a total of seven on them.
In the figure, given a net to make dice (cube). The numbers inserted in each square indicate the number of dots in it.
Insert suitable numbers in each blank so that numbers opposite faces of the die have a total of seven dots.


1823626_e4eafadcf6ea428596fdc2e0f302148a.png

Shown above is the figure where the numbers are inserted such that the numbers in opposite faces of the die have a total of seven dots
In the given cube net, $$4$$ lies opposite to $$3$$, $$6$$ lies opposite to $$1$$ and $$5$$ lies opposite to $$2$$.

1747017_1823626_ans_de70ab45b6294ecb987048fe240f61de.png


Identify if the net in the figure can be used to form a cube:


1823470_c2dff03892ae44b9a4d24a23804eda0c.png

In the given figure, the net can be folded into a cube when its faces are folded one over the other
Therefore, it is a cube net


Draw at least three different nets for making cube.

A cube net is defined as the net in which if all the faces are folded over other, they make up a perfect cube
1747002_1823488_ans_923f41a544224b00871ca8337331a065.png


Identify if the net in the figure can be used to form a cube:

1823475_a645dbfd12384088952805fd3e72388c.png

In the given figure, the net cannot be folded into a cube by folding the six faces of the net
Therefore, it is not a cube net


A cubical box is $$6cm\times 4cm\times 2cm$$ . Draw two different nets of it.


1780282_1839600_ans_da9eac93c2f64ba09f6589da3e85267b.png


Identify if the net in the figure can be used to form a cube:
1830981_d2462dc6238b45188fd5eb8a899f68cf.png

In the given figure the net can not be used to form cubes. As rectangle are of different size.


Fill in the blank:
____ sketch focus on the front view of an object.


2060402_1947066_ans_0ae189d20a264bcfa3bc8c5e7824ac0d.jpg


The sheet which divides the paper in small equilateral triangle made up of dots or lines is called _______.


2049702_1947084_ans_aec0369cd7a5435b85aaa7a717da2737.jpg


Draw nets for each of the following polyhedrons:

1673225_3b5c356bc8ae46f6aaf4fd1a33f9c095.png


2039817_1673225_ans_8a0215b3e0944ea18bbff54a5b027546.jpg


Class 7 Maths Extra Questions