GSEB Class 7 Maths Solutions Chapter 15 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: The nets that can be utilized to create cubes are (ii), (iii), (iv), and (vi). Each of these configurations allows for folding into a closed, six-faced cube.
In simple words: Nets (ii), (iii), (iv), and (vi) are the right shapes to fold into a cube.

Exam Tip: To identify if a net forms a cube, ensure it has exactly six squares, and when folded, no faces overlap and all faces are enclosed. Visualizing the fold or numbering adjacent faces can help.

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: Here are the completed nets for the dice, ensuring that the numbers on opposite faces sum to 7. The missing numbers have been filled in accordingly.

Exam Tip: When working with dice nets, visualize folding the net into a cube. Remember that faces separated by two other faces on a flat net are often opposite. If faces are adjacent, they cannot be opposite.

Question 3. Can this be a net for a die? Explain your answer.

Answer: No, this cannot be a net for a die. This is because one set of opposite faces would show 1 and 4, which sums to 5, not 7. Additionally, another pair of opposite faces would have 3 and 6, which adds up to 9, not 7. For a die, all opposite pairs must total seven.
In simple words: No, this net won't make a proper die. When folded, the numbers on opposite sides won't always add up to 7, which is a key rule for dice.

Exam Tip: To verify a die net, identify potential opposite faces by skipping one face in a linear strip. Ensure each pair sums to 7. If any pair does not, it's not a valid die net.

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

Answer: The incomplete net shown has three squares. To complete it into a net for a cube, three more squares must be added in suitable positions. Two different ways to complete the net for a cube are illustrated in the diagrams below. Each completed net contains six faces, forming a closed cube.

Exam Tip: When completing a net for a cube, always ensure the final net has six squares. A useful trick is to visualize one square as the base, and then arrange the other five around it so they can fold up to form the sides and top without gaps or overlaps.

Question 5. Match the nets with appropriate solids:

Answer: The correct matches between the solids and their corresponding nets are as follows:
(a) Cube → Net (i)
(b) Cylinder → Net (ii)
(c) Cone → Net (iii)
(d) Square Pyramid → Net (iv)
In simple words: We connect each 3D shape with the flat pattern that can be folded to make it. A cube matches the cross-shape net, a cylinder matches the rectangle with two circles, a cone matches the sector with one circle, and a pyramid matches the square with four triangles.

Exam Tip: To match solids with nets, remember the number and shape of the faces. For example, a cube has six square faces, a cylinder has two circular bases and one rectangular side (when flattened), a cone has one circular base and one curved surface (a sector when flattened), and a pyramid has a polygon base and triangular sides.