*Exercise-15.1*

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

** **

**Solution:**

Cube’s nets are (2), (3), (4) and (6).

*Q.2. There are dots on each side of a cubical dice. The sum of the dots on opposite sides of the dice is 7.Two shapes are given with empty boxes which constitute a dice. Fill the empty boxes with a suitable number such that the sum of the numbers on the opposite sides should be equal to 7.*

*Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7.*

* *

**Solution:**

* *

*Q.3.Is the given figure forms a die? Justify your answer.*

* *

**Solution:** 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.Make a cube from the incomplete net that is given in the figure. Note that a cube has 6 faces and make this cube in two ways. *

**Solution:** There are three faces given:

*Q.5. Match the nets with appropriate solids:*

* *

**Solution:**

* *

*Exercise-15.2*

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

**Solution:**

**(i) and (ii)**

**(iii) and (iv)**

*Q.2. The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.*

* *

**Solution: **The dimensions of given cuboid are 5 cm, 3 cm and 2 cm:

Three different isometric sketches are:

*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.*

**Solution: **

Oblique sketch:

Isometric sketch:

*Q.4. Make an oblique sketch for each one of the given isometric shapes:*

**Solution:**

Oblique sketches:

*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 of dimension 4 cm .*

**Solution:**

(a)A cuboid of dimension 5 cm, 3 cm and 2 cm.

(b) A cube of dimension 4 cm .

*Q.6. An isometric sheet is attached at the end of the book. You could try to make some cubes or cuboids of dimensions specified by your friend.*

**Solution:** Cubes and cuboids shapes on the isometric sheet are given below:

You can also draw more shapes of cubes and cuboids.

* Exercise-15.3*

*Q.1. When you are given a vertical cut and horizontal cut, what type of cross sections would you get?*

* (a)A brick*

*(b) An apple*

*(c) A die*

*(d) A circular pipe*

**Solution:**

** **

** 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).*

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* Solution:*

*Q.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)*

**Solution:**

*Q.3. Examine if the following are true or false: *

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

*(b) The cube can cast a shadow in the shape of a hexagon.*

**Solution:**

(a)True

(b)False

Excellent effort on student’s education

Very useful for teachers as well as students to understand the easy way of solving

Thanks:)