CBSE Class 8 Maths Visualising Solids Shapes HOTs

HOTS

Question. Which solid figures do the following nets represent?

Answer : a. Rectangular Pyramid
b. Hexagonal Pyramid
c. Hexagonal Prism 
d. Cuboid 

Question. Dice are cubes, where the numbers on the opposite faces must total 7. Which of the following is a die?

Answer : A

Question. Draw the net for the following cuboids whose dimensions are
a. length = 2 cm. breadth = 1.5 cm. height = 1 cm
b. length = 3 cm, breadth = 2 cm. height = 1.5 cm

Question. Which two of these shapes will fit together to make a cube? 

Answer : a and d

Very Short Answer type Questions

Question. Find the sum of dots visible in this dice.
Answer : 6

Question. What is the shape of bangle?
Answer : Cylinder

Question. Find the no. of faces in a Prism with triangle base.
Answer : 5

Question. Find the no. of edges in a triangular Prism.
Answer : 9

Question. A polyhedron has 7 faces and 10 vertices. Find its no. of edges.
Answer : 15

Question. Name the polygon formed in the front side of the figure.
Answer : Pentagon

Question. Name the shape and also tell the type of the given figure.

Answer : Cuboid, 3-D

Question. Find 3-D figures from the following ball, cylinder, triangle.
Answer : Ball, cylinder

Question. How many no. of squares are visible in the top, view of the given figure.

Answer : 6

Question. Find the odd one out : book, cylinder, square, cone.
Answer : Square

Question. Find the no. of edges in a match box.
Answer : 12.

Question. Find the no. of faces in a Prism with square base.
Answer : 6

Question. Find the no. of faces in a Pyramid with hexagonal base.
Answer : 7

CHALLENGES

1. a. Suppose you glue two congruent cubes face to face. How many different shapes can you make?
b. Suppose you glue three congruent cubes face to face. How many different shapes can you make?
c. Suppose you glue four congruent cubes face to face. How many different shapes can you make?
d. Verify Euler's formula for each solid obtained.

2. Suppose using 27 unit cubes, we make a 3×3×3 cube and paint its outer surface blue. If we dismantle all the 27 cubes, how many will have one blue face? How many will have two blue faces? How many will have three blue faces? Are there any with more than three blue faces?

3. Do the previous problem with 64 unit cubes, constructing a 4×4×4 cube. Can you get a general rule?

4. Consider the eight vertices of the unit cube. Taking any 3 at a time, form all possible triangles. How many equilateral triangles are there? How many right-angled triangles are there? How many isosceles triangles are there?

5. Take a pyramid with hexagonal base. Verify Euler's formula for it.

6. Consider a prism having pentagonal base. Verify Euler's formula for it.

SUMMARY

1. A solid shape bounded by polygons is called a polyhedron.

2. Two-dimensional figures like squares, rectangles, triangles and parallelograms have only two dimensions-length and breadth.

3. A solid is a three-dimensional figure which has three dimensions-length, breadth and height. It occupies space. e.g., a cuboid, a cube, a pyramid, a prism.

4. If F, E and V represent number of faces, number of edges and number of vertices respectively of a polyhedron, then
F+V–E = 2
It is known as Euler's formula.

5. A prism is a polyhedron whose two faces are identical polygons and whose side faces are rectangles.

6. A pyramid is a polyhedron whose base is a polygon of any number of sides and whose other faces are triangles with a common vertex.

7. A prism is called a regular prism if its ends are regular polygons.

8. A prism or pyramid is named after its base. A hexagonal prism or pyramid has hexagon as its base.

ERROR ANALYSIS

1. Some students don’t visualise solid shapes mainly prism and pyramid. They cram number of faces, vertices and edges rather than understand.
2. Some times they are not clear about polyhedron.

ACTIVITY

To get a net of a cuboid

Steps
1. Take a cardboard box (as shown in fig. (i)).
2. Cut out some edges to lay the box flat (as shown in fig. (ii)). 

Thus, we get a net of a cuboid by suitably cutting the edges. Note that a net of a 3-D object is a 2-D shape cut from a cardboard or thick paper which on folding forms a 3-D shape.
Different 3-D objects have different nets. Moreover, net of a 3-D shape may not be unique.
The figure below shows an open cone. We can get a net for a cone by cutting a slit along its slant surface. 

Given below are nets of some 3-D objects: