1. Identify the nets which can be used to make cubes (cut out copies of the nets and try it):
(i)
ii)
iii)
iv)
1. Identify the nets which can be used to make cubes (cut out copies of the nets and try it):
(i)
ii)
iii)
iv)
Solution:
i) When we start folding the given net like this, as shown below
After folding it will look like this.
It is not possible to fold the above given net into a dice.
(ii)
When we start folding the given net like this, as shown below
After folding it will look like this.
It is possible to fold the above given net into a dice.
(iii)When we start folding the given net like this, as shown below
After folding it will look like this.
It is possible to fold the above given net into a dice.
(iv) When we start folding the given net like this, as shown below
After folding it will look like this.
It is possible to fold the above given net into a dice.
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.
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.
Solution:
(i)
When we write the numbers as shown above the above given net will form a dice. The numbers in opposite faces have sum equal to 7 as shown step by step.
So, it is possible to fold the above given net into a dice.
(ii)
When we write the numbers as shown above the above given net will form a dice. The numbers in opposite faces have sum equal to 7 as shown step by step.
So, it is possible to fold the above given net into a dice.
3.Can this be a net for a die?
Explain your answer.
3.Can this be a net for a die?
Explain your answer.
Solution:
The answer is NO, because one face will contain 4 and opposite to this there is a face which contains 1 whose summation is not equal to 7, and in another pair of one face will contain 6 and opposite to this there is a face that contain 3 whose summation is not equal to 7.
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.)
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.)
Solution:
The three faces that are possible is shown in the above shapes.
5.Match the nets with appropriate solids:
5.Match the nets with appropriate solids:
Solution:
(a) This solid matches appropriately with - (ii)
(b) This solid matches appropriately with - (iii)
(c) This solid matches appropriately with - (iv)
(d) This solid matches appropriately with - (i)
6. The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.
6. The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.
Solution:
Cuboid dimensions given- 5 cm, 3 cm, and 2 cm.
The different kind of isometric sketches of cuboid are drawn below as a,b,c.
(a)
(b)
(c)
7. 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.
7. 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.
Solution:
Its isometric sketch will look like this-
Its Oblique sketch will look like this-
8. Make an oblique sketch for each one of the given isometric shapes:
(i)
(ii)
8. Make an oblique sketch for each one of the given isometric shapes:
(i)
(ii)
Solution:
(i) Its Oblique sketch will look like this-
(ii) Its Oblique sketch will look like this-
9. 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.
9. 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.
Solution:
(a)
(i) Its Isometric sketch will look like this-
(ii) Its Oblique sketch will look like this-
(b)
(i) Its Isometric sketch will look like this-
(ii) Its Oblique sketch will look like this-
10. What cross-sections do you get when you give a
(i) vertical cut (ii) horizontal cut
to the following solids?
10. What cross-sections do you get when you give a
(i) vertical cut (ii) horizontal cut
to the following solids?
Solution:
(a) A brick
When we cut the brick vertically, it looks like this-
When we cut the brick horizontally, it looks like this-
(b) A round apple
When we cut the apple horizontally, it looks like this-
When we cut the apple vertically, it looks like this-
(c) A die
When we cut the dice horizontally, it looks like this-
When we cut the dice vertically, it looks like this-
(d) A circular pipe
When we cut the pipe vertically, it looks like this-
When we cut the pipe horizontally, it looks like this-
(e) An ice cream cone
When we cut the cone vertically, it looks like this-
When we cut the cone horizontally, it looks like this-
11. 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)
11. 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)
Solution:
(i) The light will cast a shadow of a circle, if light beam hits from top of the ball.
(ii) The light will cast a shadow of a rectangle, if light beam hits from top of the cylinder.
(iii) The light will cast a shadow of a rectangle, if light beam hits from top of the book.
12. 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)
12. 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)
Solution:
(i) Football, Disc, Bangles etc gives the shadow as circle.
(ii) Dice, Chess Board, Bread etc gives a shadow of square.
(iii) Ice-cream Cone, Party cap, Tent etc gives a shadow of triangle.
(iv) Mobile, Laptop, Brick, etc gives a shadow of rectangle.
13. 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.
13. 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.
Solution:
(i) Above statement is True, because when the light beam hits straight from the top surface of cube it cast a shadow of a rectangle.
(ii) Above statement is False, because hexagon contains 6 sides and square contains only 4 sides. It is not possible to create a 6 sides shadow from a cube.
