NCERT Solutions Class 7 Maths Chapter 13 Visualising Solid Shapes

4.0NCERT Questions with Solutions for Class 7 Maths Chapter 13 - Detailed Solutions

Exercise: 13.1

• 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)

• Sol. Cubes nets are (ii), (iii), (iv) and (vi).
• Dice are cubes with dots on each face. Opposite faces of a dice always have a total of seven dots on them. Here are two nets to make dice (cube); 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 . Sol.

• Can this be a net for a dice? Explain your answer.
  
  Sol. No, this cannot be a net for a die. Because one pair of opposite faces will have 1 and 4 on them and another pair of opposite faces will have 3 and 6 on them whose total is not equal to 7 .
• 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.)
  
  Sol. There three faces are given:
  
• Match the nets with appropriate solids:
  
  Sol.
  

Exercise: 13.2

• Use isometric dot paper and make an isometric sketch for each one of the given shapes: (i)
  
  (ii)
  
  (iii)
  
  (iv)
  
  
  Sol. (i)
  
  (ii)
  
  (iii)
  
  (iv)
  
• The dimensions of a cuboid are $5\mathrm{cm},3\mathrm{cm}$ and 2 cm . Draw three different isometric sketches of this cuboid. Sol. The dimensions of given cuboid are 5 cm , 3 cm and 2 cm : Three different isometric sketches are:
  
• Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric of this cuboid. Sol. Oblique sketch
  
  Isometric sketch
  
• Make an oblique sketch for each one of the given isometric shapes:
  
  Sol.
  
  (a)
  
  (b)
• Give (i) an oblique sketch and (ii) an isometric sketch for each of the following: (a) A cuboid of dimensions $5\mathrm{cm},3\mathrm{cm}$, and 2 cm . (Is your sketch unique?) (b) A cube with an edge 4 cm long. Sol. (a) A cuboid of dimension $5\mathrm{cm},3\mathrm{cm}$ and 2 cm .
  
  (i) Oblique sketch
  
  (ii) Isometric sketch (b) A cube with an edge 4 cm long. (i) Oblique sketch
  
  (ii) Isometric sketch
  

Exercise: 13.3

• 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 Sol.
  

Exercise: 13.4

• A bulb is kept burning just 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). Sol.
  
• 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!) Sol.
  
• 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. Sol. (i) True (ii) False Cubes and cuboids shapes on isometric sheet are given below: