Visualising Solid Shapes
Class 7th Mathematics CBSE Solution
- Identify the nets which can be used to make cubes (cut out copies of the nets…
- Dice are cubes with dots on each face. Opposite faces of a die always have a…
- Can this be a net for a die? Explain your answer. |c|c| 1&2 3&4 &5&6…
- Here is an incomplete net for making a cube. Complete it in at least two…
- Match the nets with appropriate solids:
- Use isometric dot paper and make an isometric sketch for each one of the given…
- The dimensions of a cuboid are 5 cm, 3 cm, and 2 cm. Draw three different…
- Three cubes each with 2 cm edge are placed side by side to form a cuboid.…
- Make an oblique sketch for each one of the given isometric shapes: 3…
- Give (i) an oblique sketch and (ii) an isometric sketch for each of the…
Exercise 15.1
Question 1.Identify the nets which can be used to make cubes (cut out copies of the nets and try it):
Answer:
(i) Can’t make a cube as folding won’t get us the front edge.
(ii) Can make a cube if we fold the bottom three upright and top three upright.
(iii) Can make a cube by folding last two sideways and top two left side ways.
(iv) Can make a cube by folding single ones to make front back and top edge.
(v) Can’t make a cube as back edge will be open on folding.
(vi) Can make a cube by folding 4 in a row left wise.
Question 2.
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.
Answer:
Since sum of opposite sides in a cube is 7.
Opposite to 5 comes 2, opposite to 4 comes 3 and opposite to 6 comes 1.
Question 3.
Can this be a net for a die? Explain your answer.
Answer:
Because,4 comes opposite to 1. They do not add up to 7.
Also 3 comes opposite to 6. They do not add up to 7.
Question 4.
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.)
Answer:
Here we have given 3 faces of cube, so we can implement other 3 faces in this way to get a cube-
Question 5.
Match the nets with appropriate solids:
Answer:
(a) As cube has 6 edges folding the 6 squares will make a cube.
(b) A cylinder is formed by rolling a cylinder with two circles at the top and bottom view.
(c) A cone is formed by rotating a triangle in 3D and a circle at the bottom/top view.
(d) A pyramid is formed by triangles.
Exercise 15.2
Question 1.Use isometric dot paper and make an isometric sketch for each one of the given shapes:
Answer:
(i)
(ii)
(iii)
(iv)
Question 2.
The dimensions of a cuboid are 5 cm, 3 cm, and 2 cm. Draw three different isometric sketches of this cuboid.
Answer:
The possible sketches are-
Question 3.
Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid.
Answer:
Here is an oblique sketch-
Here is isometric sketch for three cubes of 2cm edge placed side by side.
Question 4.
Make an oblique sketch for each one of the given isometric shapes:
Answer:
Here are the oblique sketches for the following-
Question 5.
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.
Answer:
(a) Oblique and isometric sketch
No it won’t be unique. Since length, height and width are not mentioned. I can draw 2 more figures. I can switch the three.
(b)-Oblique sketch for a cube of side =4cm.
Isometric sketch for the same cube-
Exercise 15.3
Question 1.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
Answer:
(a) Brick: It is rectangular so any cut will get a rectangle.
(i) A rectangle in a vertical cut.
(ii) A rectangle in a horizontal cut.
(b) A round figure:Itwill cut to a circle in both ways.
(i) Circle in vertical cut.
(ii) Circle in a horizontal cut.
(c) A die: It is a cube and hence is a 3D representation of a square.
(i)A square in vertical cut.
(ii) A square in a horizontal cut.
(d)- A pipe: It is cylindrical and will cut to rectangle and square in a different case.
(i) A rectangle in a vertical cut.
(ii) Circle in a horizontal cut.
(e)- A cone. It will cut to triangle and circle in a different case.
(i)Triangle in vertical cut.
(ii)Circle in horizontal cut.
Exercise 15.4
Question 1.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).
Answer:
Question 2.
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!)
Answer:
(i) Spherical, (ii) Cube, (iii) Pyramid, (iv)Cuboid.
(i) Sphere is formed by rotating a circle in 3D.
(ii) Cube shadows to a square in 2D.
(iii) A triangle is formed by image of a pyramid.
(iv) A cuboid is 3D representation of rectangle.
Question 3.
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.
Answer:
A cube can cast shadow only in the shape of square. So hexagon is not possible. Since a surface of cube is square from any view (side or top view).