NCERT Solutions Class 7 Mathematics Chapter 15 Visualizing Solid Shapes

Exercise 15.1

Q.1) Identify the nets which can be used to make cubes (cut out copies of the nets and try it):

Sol.3) 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.

Q.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 faces are there in the net here? (Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.)

Exercise 15.2

Q.1) Use isometric dot paper and make an isometric sketch for each one of the given shapes :

Q.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.
Sol.3) Oblique sketch

Q.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.
An isometric sheet is attached at the end of the book. You could try to make on it some cubes or cuboids of dimensions specified by your friend.
Sol.5) (a) A cuboid of dimension 5 cm, 3 cm and 2 cm.
(i) Oblique sketch (ii) Isometric sketch

Q.6) An isometric sheet is attached at the end of the book. You could try to make on it some cubes or cuboids of dimensions specified by your friend.
Sol.6) Cubes and cuboids shapes on isometric sheet given below

Exercise 15.3

Q.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.

Exercise 15.4

Q.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).

Q.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!).

Q.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.
Sol.3) It can be verified only when you take a cube inside a dark room and try to throws light by using torch on the cube from different angles, corners and positions.
i) True
ii) False