GSEB Class 7 Maths Solutions Chapter 15 Visualising Solid Shapes InText Questions

Try These (Page 277)

Question. Match the shape with the name:
(i) (Cylinder image)
(ii) (Sphere image)
(iii) (Cube image)
(iv) (Cuboid image)
(v) (Pyramid image)
(vi) (Cone image)
(a) Cuboid
(b) Cylinder
(c) Cube
(d) Sphere
(e) Pyramid
(f) Cone
Answer:
(i) – (b) Cylinder
(ii) – (d) Sphere
(iii) – (c) Cube
(iv) – (a) Cuboid
(v) – (e) Pyramid
(vi) – (f) Cone
In simple words: To find the right shape for each name, we look at their forms. The cylinder is like a can, the sphere is like a ball, the cube is a perfect box, the cuboid is a longer box, the pyramid has a point and a square base, and the cone is like a party hat.

Exam Tip: When matching shapes with names, carefully look at their features like flat faces, curved surfaces, and pointed tops to identify them correctly.

Do This (Page 279)

Question 1. Complete the following table:
Answer: The completed table showing the faces, edges, and vertices for different solids is given below:

In simple words: This table shows the counts of flat surfaces (Faces), lines where surfaces meet (Edges), and points where lines meet (Vertices) for different 3D shapes. You need to fill in the missing numbers.

Exam Tip: Remember Euler's formula, \( F + V - E = 2 \), to cross-check the number of faces, vertices, and edges for any polyhedron.

Try These (Page 281)

Question 1. Here you find four nets. There are two correct nets among them to make a tetrahedron. See if you can work out which nets will make a tetrahedron.
(i) (Net image)
(ii) (Net image)
(iii) (Net image)
(iv) (Net image)
Answer: (i) and (iii) are correct nets that will make a tetrahedron.
In simple words: When you fold the first net (i) and the third net (iii), they both form a tetrahedron, which is a shape with four triangular faces.

Exam Tip: To identify correct nets, imagine folding along the lines; ensure all faces connect perfectly without gaps or overlaps to form the 3D shape.

Try These (Page 286)

Question 1. Try to guess the number of cubes in the following arrangements.
(i) (Arrangement of cubes image)
(ii) (Arrangement of cubes image)
(iii) (Arrangement of cubes image)
Answer:
(i) There are 24 cubes.
(ii) There are 8 cubes.
(iii) There are 9 cubes.
In simple words: You need to count the total number of small blocks (cubes) in each stack. In the first picture, there are 24 cubes; in the second, there are 8 cubes; and in the third, there are 9 cubes.

Exam Tip: When counting cubes in a stack, remember to count hidden cubes that support those visible on top, often by visualizing layers.

Try These (Page 287)

Question 1. Two dice are placed side by side as shown: Can you say what the total would be on the face opposite to
(Image of two dice)
(a) 5 + 6
(b) 4 + 3
(Remember that in a die sum of numbers on opposite faces is 7.)
Answer:
(a) The total opposite to face \( 5 + 6 \) is \( 2+1 \), which is \( 3 \).
(b) The total opposite to face \( 4 + 3 \) is \( 3+4 \), which is \( 7 \).
In simple words: Since opposite faces on a standard die always add up to 7, for 5+6, the opposite faces would be 2+1, giving a total of 3. For 4+3, the opposite faces would be 3+4, giving a total of 7.

Exam Tip: Always recall the basic property of a standard die: the sum of the numbers on opposite faces is always seven.

Question 2. Three cubes each with 2 cm edge are placed side by side to form a cuboid. Try to make an oblique sketch and say what could be its length, breadth and height.
(Image of oblique sketch of three cubes)
Answer:
Length of the cuboid = \( 2 \text{ cm} + 2 \text{ cm} + 2 \text{ cm} = 6 \text{ cm} \).
Breadth of the cuboid = \( 2 \text{ cm} \).
Height of the cuboid = \( 2 \text{ cm} \).
In simple words: When three cubes, each with a 2 cm side, are put next to each other in a row, they form a bigger shape called a cuboid. The total length of this new shape will be 6 cm (because 2+2+2=6), but its width and height will remain 2 cm, just like the original cubes.

Exam Tip: When combining identical solid shapes, remember that only the dimension along which they are joined will change; other dimensions remain the same.

Try These (Page 291)

Question 1. For each solid, the three views (1), (2), (3) are given. Identify for each solid the corresponding top, front and side views.
(a) Solid image with its three views
(b) Solid image with its three views
(c) Solid image with its three views
(d) Solid image with its three views
Answer: The identification of the corresponding top, front, and side views for each solid is:
(a) (1) is the Front view, (2) is the Side view, (3) is the Top view.
(b) (1) is the Top view, (2) is the Side view, (3) is the Front view.
(c) (1) is the Side view, (2) is the Front view, (3) is the Top view.
(d) (1) is the Side view, (2) is the Top view, (3) is the Front view.
In simple words: For each 3D object shown, you need to match the numbered pictures (1, 2, 3) to whether they show the object from the front, from the side, or from above.

Exam Tip: Practice visualizing 3D objects from different angles; remember that the front, side, and top views show only two dimensions of the object at a time.

Question 2. Draw a view of each solid as seen form the direction indicated by the arrow.
(i) Solid image with arrow
(ii) Solid image with arrow
(iii) Solid image with arrow
Answer: The views for each solid, when seen from the direction of the arrow, are shown below:
(i)(ii)(iii)
In simple words: The pictures above show what each solid looks like when you view it from the direction the arrow points.

Exam Tip: Pay close attention to the arrow's direction to accurately determine which face or combination of faces will be visible in the requested view.