Samacheer Kalvi Class 8 Maths Solutions Chapter 2 Measurements Exercise 2.3

Question 1. Fill in the blanks:
(i) The three dimensions of a cuboid are ______, ______, and ______.
(ii) The meeting point of more than two edges in a polyhedron is called as ______.
(iii) A cube has ______ faces.
(iv) The cross section of a solid cylinder is ______.
(v) If a net of a 3-D shape has six plane squares, then it is called ______.
Answer:
(i) The three dimensions of a cuboid are **length**, **breadth**, and **height**. These three measurements define the size of any rectangular solid.
(ii) The meeting point of more than two edges in a polyhedron is called as **vertex**.
(iii) A cube has **six** faces. Each face is a perfect square.
(iv) The cross section of a solid cylinder is a **circle**. If you slice a cylinder straight across, you will always see a circle.
(v) If a net of a 3-D shape has six plane squares, then it is called a **cube**. A cube is a special type of cuboid where all sides are equal.
In simple words: A cuboid needs length, width, and height. Where edges meet is called a vertex. A cube has six flat sides. Slicing a cylinder gives a circle. Six square sides make a cube.

🎯 Exam Tip: Remember these basic definitions for 3-D shapes as they are fundamental to understanding geometry. Visualizing the shapes can help a lot.

Question 2. Match the following
(i)
 

Question 3. Which 3 - D shapes do the following nets represents? Draw them.
(i)
Answer: The net in part (i) represents a **cube**. A cube is a 3D shape with six identical square faces, making all its sides equal in length. This means it is perfectly symmetrical.
In simple words: This net shows a cube. A cube has 6 square faces that are all the same size.

🎯 Exam Tip: Practice visualizing how different 2D nets fold up into 3D shapes. Knowing the number and type of faces is key.

(ii)
Answer: The net in part (ii) represents a **cuboid**. A cuboid is a 3D shape with six rectangular faces, where opposite faces are identical. It's like a stretched cube.
In simple words: This net shows a cuboid. A cuboid is like a box with rectangular sides.

🎯 Exam Tip: Understand that cuboids are similar to cubes but have different dimensions for their faces. Pay attention to whether the faces are squares or rectangles.

(iii)
Answer: The net in part (iii) represents a **triangular prism**. A triangular prism has two triangular bases and three rectangular side faces. It's like a triangle stretched into a 3D shape.
In simple words: This net forms a triangular prism. It has two triangle ends and three rectangle sides.

🎯 Exam Tip: Identify the base shape of a prism first, then count the number of rectangular faces to confirm the type of prism.

(iv)
Answer: The net in part (iv) represents a **square pyramid**. A square pyramid has a square base and four triangular faces that meet at a single point (apex). It looks like an Egyptian pyramid.
In simple words: This net makes a square pyramid. It has a square at the bottom and four triangles that meet at the top.

🎯 Exam Tip: Pyramids have one base and triangular faces that meet at a point. The name of the pyramid comes from the shape of its base.

(v)
Answer: The net in part (v) represents a **cylinder**. A cylinder has two circular bases and one curved rectangular side when unrolled. It resembles a can or a pipe.
In simple words: This net forms a cylinder. It has two circles as its ends and a curved side.

🎯 Exam Tip: Remember that a cylinder has curved surfaces and circular bases, which are key distinguishing features.

Question 4. For each solid, three views are given. Identify for each solid, the corresponding Top, Front and Side (T, F and S) views.

Answer: The table above correctly identifies the Top (T), Front (F), and Side (S) views for each given solid. These views help in understanding the three-dimensional structure of an object from different angles. Knowing these views is important for technical drawings and design.
In simple words: The table shows how each 3D shape looks from the top, front, and side. This helps us fully understand what the object looks like.

🎯 Exam Tip: When identifying views, imagine looking directly at the object from each specified direction (top, front, side) and drawing only what you would see from that perspective.

Question 5. Verify Euler's formula for the table given below.

Answer: Euler's formula states that for any polyhedron, the number of Faces (F), Vertices (V), and Edges (E) are related by the equation: \( F + V - E = 2 \). This formula helps describe the structure of 3D objects.
(i) \( F = 4 \); \( V = 4 \); \( E = 6 \)
\( F + V - E = 4 + 4 - 6 = 8 - 6 = 2 \)
\( \implies \) Euler's formula is satisfied.
(ii) \( F = 10 \); \( V = 6 \); \( E = 12 \)
\( F + V - E = 10 + 6 - 12 = 16 - 12 = 4 \)
\( \implies 4 \neq 2 \)
\( \implies \) Euler's formula is not satisfied.
(iii) \( F = 12 \); \( V = 20 \); \( E = 30 \)
\( F + V - E = 12 + 20 - 30 = 32 - 30 = 2 \)
\( \implies \) Euler's formula is satisfied.
(iv) \( F = 20 \); \( V = 13 \); \( E = 30 \)
\( F + V - E = 20 + 13 - 30 = 33 - 30 = 3 \)
\( \implies 3 \neq 2 \)
\( \implies \) Euler's formula is not satisfied.
(v) \( F = 32 \); \( V = 60 \); \( E = 90 \)
\( F + V - E = 32 + 60 - 90 = 92 - 90 = 2 \)
\( \implies \) Euler's formula is satisfied.
In simple words: We check Euler's rule which says Faces + Vertices - Edges should always equal 2. For each example, we add the faces and vertices, then subtract the edges. If the answer is 2, the rule works for that shape.

🎯 Exam Tip: Make sure to correctly identify F (faces), V (vertices), and E (edges) from the given data before applying Euler's formula. A common mistake is miscounting these elements.