Class 7 - Maths - Visualising Solid Shapes

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) The given net can be folded as follows: When the faces that are in the sky blue colour and in pink colour are folded to make a cube,

they will be overlapping each other.

(ii) The given net can be folded as follows: A cube can thus be formed in the above way.

(iii) The given net can be folded as follows: A cube can thus be formed in the above way.

(iv) The given net can be folded as follows: A cube can thus be formed in the above way.

(v) The given net can be folded as follows: When the faces that are in the blue colour and in red colour are folded to make a cube,

they will be overlapping each other.

(vi) The given net can be folded as follows: A cube can thus be formed in the above way.

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:

(i) The number can be inserted as follows so as to make the given net into a net of a dice. It can be observed that the sum of the opposite faces is 7

(ii) The number can be inserted as follows so as to make the given net into a net of a dice. Question 3:

Can this be a net for a die? Explain your answer. Answer:

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.

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

There are 3 faces in the given net. The given net can be completed as follows.  Question 5:

Match the nets with appropriate solids: Answer: 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 dimensions of given cuboid are 5 cm, 3 cm and 2 cm: Three different isometric 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:

Oblique sketch: Isometric sketch: Question 4:

Make an oblique sketch for each one of the given isometric shapes: Answer:

Oblique sketches: 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) A cuboid of dimension 5 cm, 3 cm and 2 cm. (b) A cube with an edge 4 cm long. Question 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.

Answer:

Cubes and cuboids shapes on isometric sheet given below: You can also draw more shapes of cubes and cuboids.

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: 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 the overhead projector.

Identify the solid (s) that match each shadow. (There may be multiple answers for these!) Answer: 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:

(i) True

The cube can cast a shadow in the shape of a rectangle.

(ii) False

A cube can cast a shadow in the shape of a rectangle.

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