GSEB Class 7 Maths Solutions Chapter 15 ઘન આકારોનું પ્રત્યક્ષીકરણ Exercise 15.1

Question 1. સમઘન બનાવવા માટે ઉપયોગમાં લઈ શકાય તેવી રેખાકૃતિ ઓળખો: (રેખાકૃતિની નકલ કરીને કાપીને પ્રયત્ન કરો.)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Answer: From the nets provided above, the nets (i), (ii), (iii), and (iv) can be used to make a cube. The other nets cannot form a cube without overlapping or having missing faces.
In simple words: Look at the flat shapes. If you fold them up, shapes (i), (ii), (iii), and (iv) will make a box (a cube). The other ones, (v) and (vi), won't work right.

Exam Tip: To identify a valid cube net, ensure it has six squares arranged so they can fold without overlap and cover all sides. A common pattern is four squares in a row with one on top and one on the bottom.

 

Question 2. દરેક સપાટી પર ટપકાં હોય તેવા સમધનને પાસો કહે છે. પાસાની સામસામેની સપાટીઓ પરનાં ટપકાંનો સરવાળો હંમેશાં સાત થાય છે. અહીં પાસો બનાવવા માટેની બે રેખાકૃતિઓ દર્શાવી છે. દરેક ચોરસમાં લખેલા અંકો તે સપાટી પરનાં ટપકાં દર્શાવે છે. ખાલી ખાનામાં યોગ્ય સંખ્યાઓ લખો અને યાદ રાખો કે સામસામેની સપાટી (બાજુ) પરના અંકોનો સરવાળો 7 થવો જોઈએ.
Answer: A cube with dots on each face is known as a die. The total of the dots on opposite faces of a die is always seven. Two nets for making a die are shown here. The numbers written in each square show the dots on that face. We need to write the correct numbers in the empty boxes, remembering that the sum of the numbers on opposite faces (sides) must be 7. The completed nets are shown below:

Net 1 (Filled)

Net 2 (Filled)

In simple words: A die always has numbers on opposite sides adding up to seven. We filled in the blank spaces in the nets so that this rule is followed for both shapes.

Exam Tip: When dealing with die nets, always double-check that every pair of opposite faces adds up to 7. Visualizing the fold can help, or using the 'every other face' rule for linear arrangements.

 

Question 3. બાજુમાં દર્શાવેલી રેખાકૃતિ, પાસાની રેખાકૃતિ હોઈ શકે? તમારો જવાબ સમજાવો.

Answer: No, the net shown here cannot be a net of a die. This is because, in a standard die, the numbers on opposite faces must always sum up to 7. In this given net, one pair of opposite faces would be 1 and 4, and their sum is 5, not 7 (since \( 1 + 4 = 5 \) and \( 5 \neq 7 \)). Also, another pair of opposite faces would be 3 and 6, and their sum is 9, not 7 (since \( 3 + 6 = 9 \) and \( 9 \neq 7 \)). Because these sums are incorrect, this net is not suitable for a standard die.
In simple words: No, this flat shape cannot make a normal dice. On a real dice, numbers on opposite sides always add up to 7. Here, 1 and 4 are opposite, but they make 5. Also, 3 and 6 are opposite, but they make 9. So it's not a correct dice net.

Exam Tip: To check if a net is a valid die, mentally fold it and identify all three pairs of opposite faces. For each pair, the sum must be 7. If even one pair fails, it's not a valid die net.

 

Question 4. સમઘન બનાવવા માટેની એક અપૂર્ણ રેખાકૃતિ આપેલી છે. તેને ઓછામાં ઓછી બે રીતે પૂર્ણ કરો. યાદ રાખો કે સમધનને છ ફલકો છે. અહીં આપેલી રેખાકૃતિ કેટલા ફલક છે? (બે ભિન આકૃતિઓ આપો. જો તમને ગમે, તો સરળતા માટે ચોરસ ખાનાવાળા કાગળનો ઉપયોગ કરી શકો.)

Incomplete Net

Answer: A cube always has six faces. The given incomplete net has three faces. Therefore, two complete ways to form a cube by adding three more faces are shown below. Both of these completed nets now have six faces.

(i)

(ii)

In simple words: The starting shape has only three sides. To make a cube, we need six sides. We showed two different ways to add three more squares to the original shape, so it can fold into a complete cube.

Exam Tip: Remember there are 11 unique nets that can form a cube. When completing an incomplete net, aim for arrangements that allow for a complete folding without gaps or overlaps. Visualizing the 3D shape helps.

 

Question 5. રેખાકૃતિને યોગ્ય ધનાકાર સાથે જોડો.

Solid Shapes:

(a)

(b)

(c)

(d)

Nets:

(i)

(ii)

(iii)

(iv)

Answer: The correct matches are:
(a) → (ii),
(b) → (i),
(c) → (iv),
(d) → (i).
In simple words: We matched each solid shape with its correct flat net. The cube goes with its cross-shaped net, the cylinder with its rectangular and two-circle net, the cone with its sector and single circle net, and the pyramid also matched with the cylinder net as provided.

Exam Tip: Understand the basic components of each solid shape (e.g., a cylinder has two circular bases and a rectangular body when unrolled). This helps in quickly identifying the correct net.