NCERT solutions for class 7 maths chapter 15 Visualising Solid Shapes
Exploring Visualising Solid Shapes Chapter 15 of NCERT Class 7 Maths, titled "Visualising Solid Shapes," offers students a profound understanding of three-dimensional geometrical figures. The chapter consists of four exercises, each packed with a variety of questions to challenge and enhance students' comprehension. This collection of NCERT Solutions for Class 7 Maths furnishes comprehensive answers to all exercises, equipping students with a valuable resource for exam preparation.
Exercise 15.1
Here is an incomplete net for making a cube. Complete it in at least two different ways. Remember that a cube has six faces. How many are there in the net here?
(Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.)
In the given net there are 3 faces and it can be completed as shown below,
Match the nets with appropriate solids:
(a) (ii)
Because, the net (ii) can be folded as a square.
(b) (iii)
Because, the net (iii) can be folded as a cylinder.
(c) (iv)
Because, the net (iv) can be folded as cone.
(d) (i)
Because, the net (i) can be folded as a pyramid.
Identify the nets which can be used to make cubes (cut out copies of the nets and try it):
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(i) The given net cannot be folded as a cube.
Because, it can be folded as below,
(ii) The given net can be folded as a cube.
Because, it can be folded as below,
(iii) The given net can be folded as a cube.
Because, it can be folded as below,
(iv) The given net can be folded as a cube.
Because, it can be folded as below,
(v) The given net cannot be folded as a cube.
Because, it can be folded as below,
(vi) The given net can be folded as a cube.
Because, it can be folded as below,
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.
(i)
By observing the above figure the sum of the opposite faces is equal to 7.
So, the given net can be folded into a net of dice.
(ii)
By observing the above figure the sum of the opposite faces is equal to 7.
So, the given net can be folded into a net of dice.
Can this be a net for a die?
Explain your answer.
The given net is folded as dice is shown in the figure below,
No, this cannot be a net for a die.
By observing the figure we can say that, one pair of opposite face will have 1 and 4, another pair of opposite face will have 3 and 6 the sum of these two opposite faces are not equal to 7.
Exercise 15.2
Make an oblique sketch for each one of the given isometric shapes:
(i)
(ii)
(i)
(ii)
The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.
It is given that the dimensions of a cuboid are 5 cm, 3 cm, and 2 cm.
The three different isometric sketches of this cuboid are shown below:
(i)
(ii)
(iii)
Use isometric dot paper and make an isometric sketch for each one of the given shapes:
(i)
(ii)
(iii)
(iv)
(i)
(ii)
(iii)
(iv)
Three cubes, each with a 2 cm edge, are placed side by side to form a cuboid. Sketch an oblique and isometric sketch of this cuboid.
Oblique sketch
Isometric sketch
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.
(a) (i) Oblique sketch
(ii) Isometric sketch
(b) (i) Oblique sketch
(ii) Isometric sketch
Exercise 15.3
What cross-sections do you get when you give a
(i) vertical cut (ii) horizontal cut
to the following solids?
(a) A brick
(b) A round apple
(c) A die
(d) A circular pipe
(e) An ice cream cone
The cross-section of a brick when it is cut into vertically is as shown in the figure below,
The cross-section of a brick when it is cut into horizontally is as shown in the figure below,
(b)
The cross-section of a round apple when it is cut into vertically is as shown in the figure below,
The cross-section of a round apple when it is cut into horizontally is as shown in the figure below,
(c)
The cross-section of a die when it is cut into vertically is as shown in the figure below,
The cross-section of a die when it is cut into horizontally is as shown in the figure below,
(d)
The cross-section of a circular pipe when it is cut into vertically is as shown in the figure below,
The cross-section of a circular pipe when it is cut into horizontally is as shown in the figure below,
(e)
The cross-section of an ice cream when it is cut into vertically is as shown in the figure below,
The cross-section of an ice cream when it is cut into horizontally is as shown in the figure below,
Exercise 15.4
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).
(i)
(ii)
(iii)
(i)
The shape of the shadow obtained from the ball is a circle.
(ii)
The shape of the shadow obtained from the cylindrical pipe is a rectangle.
(iii)
The shape of the shadow obtained from the book is a rectangle.
Here are the shadows of some 3-D objects, when seen under the lamp of an overhead projector. Identify the solid(s) that match each shadow. (There may be multiple answers for these!)
(i)
(ii)
(iii)
(iv)
(i) Cricket ball, water bottle cap, Disc
(ii) Die, chalk box etc.
(iii) Birthday cap, pizza slice etc.
(iv) Book, keyboard, mobile etc.
Examine if the following are true statements:
(i) The cube can cast a shadow in the shape of a rectangle.
(ii) The cube can cast a shadow in the shape of a hexagon.
(i) The above statement is true.
(ii) The above statement is false.
| K12 Techno Services ®
ORCHIDS - The International School | Terms | Privacy Policy | Cancellation