Chapters
Chapter 2: Measurements
Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 2 Measurements Exercise 2.1 [Pages 58 - 59]
Fill in the blanks:
The ratio between the circumference and diameter of any circle is _______
A line segment which joins any two points on a circle is a ___________
The longest chord of a circle is __________
The radius of a circle of diameter 24 cm is _______
A part of circumference of a circle is called as _______
Match the following:
Column A | Column B |
(i) Area of a circle | (a) `1/4 pi"r"^2` |
(ii) Circumference of a circle | (b) (π + 2)r |
(iii) Area of the sector of a circle | (c) πr^{2} |
(iv) Circumference of a semicircle | (d) 2πr |
(v) Area of a quadrant of a circle | (e) `theta^circ/360^circ xx pi"r"^2` |
Find the central angle of the shaded sectors (each circle is divided into equal sectors).
Sectors | ||||
Central angle of each sector (θ°) |
For the sectors with given measures, find the length of the arc, area and perimeter. (π = 3.14)
central angle 45°, r = 16 cm
For the sectors with given measures, find the length of the arc, area and perimeter. (π = 3.14)
central angle 120°, d = 12.6 cm
From the measures given below, find the area of the sectors.
Length of the arc = 48 m, r = 10 m
From the measures given below, find the area of the sectors.
length of the arc = 50 cm, r = 13.5 cm
Find the central angle of the sectors whose measures are given below. `(π = 22/7)`
area = 462 cm^{2}, r = 21 cm
Find the central angle of the sectors whose measures are given below. `(π = 22/7)`
length of the arc = 44 m, r = 35 m
A circle of radius 120 m is divided into 8 equal sectors. Find the length of the arc of each of the sectors
A circle of radius 70 cm is divided into 5 equal sectors. Find the area of each of the sectors
Dhamu fixes a square tile of 30 cm on the floor. The tile has a sector design on it as shown in the figure. Find the area of the sector. (π = 3.14)
A circle is formed with 8 equal granite stones as shown in the figure each of radius 56 cm and whose central angle is 45°. Find the area of the granite stones. `(pi = 22/7)`
Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 2 Measurements Exercise 2.2 [Pages 65 - 66]
Find the perimeter and area of the figure given below. `(pi = 22/7)`
Find the perimeter and area of the figure given below. `(pi = 22/7)`
Find the area of the shaded part in the following figure. (π = 3.14)
Find the area of the shaded part in the following figure. (π = 3.14)
Find the area of the combined figure given which is got by joining of two parallelograms
Find the area of the combined figure given, formed by joining a semicircle of diameter 6 cm with a triangle of base 6 cm and height 9 cm. (π = 3.14)
The doormat which is in a hexagonal shape has the following measures as given in the figure. Find its area.
A rocket drawing has the measures as given in the figure. Find its area
Find the area of the irregular polygon shaped fields given below.
Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 2 Measurements Exercise 2.3 [Pages 71 - 72]
Fill in the blanks:
The three dimensions of a cuboid are ____, _____ and ____
The meeting point of more than two edges in a polyhedron is called as ______
A cube has __________ faces
The cross section of a solid cylinder is __________
If a net of a 3-D shape has six plane squares, then it is called ______
Match the following:
Match the following:
Column A | Column B | ||
(i) | (a) | Cylinder | |
(ii) | (b) | Cuboid | |
(iii) | (c) | Triangular Prism | |
(iv) | (d) | Square Pyramid |
Which 3-D shapes do the following nets represent? Draw them
Which 3-D shapes do the following nets represent? Draw them
Which 3-D shapes do the following nets represent? Draw them
Which 3-D shapes do the following nets represent? Draw them
Which 3-D shapes do the following nets represent? Draw them
For each solid, three views are given. Identify for each solid, the corresponding Top, Front and Side (T, F and S) views.
Verify Euler’s formula for the table given below.
Faces | Verticles | Edges |
4 | 4 | 6 |
Verify Euler’s formula for the table given below.
Faces | Verticles | Edges |
10 | 6 | 12 |
Verify Euler’s formula for the table given below.
Faces | Verticles | Edges |
12 | 20 | 30 |
Verify Euler’s formula for the table given below.
Faces | Vertices | Edges |
20 | 13 | 30 |
Verify Euler’s formula for the table given below.
Faces | Vertices | Edges |
32 | 60 | 90 |
Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 2 Measurements Exercise 2.4 [Pages 72 - 73]
Miscellaneous Practice Problems
Two gates are fitted at the entrance of a library. To open the gates easily, a wheel is fixed at 6 feet distance from the wall to which the gate is fixed. If one of the gates is opened to 90°, find the distance moved by the wheel (π = 3.14)
With his usual speed, if a person covers a circular track of radius 150 m in 9 minutes, find the distance that he covers in 3 minutes (π = 3.14)
Find the area of the house drawing given in the figure
Draw the top, front and side view of the following solid shapes
Draw the top, front and side view of the following solid shapes
Challenging problems
Guna has fixed a single door of width 3 feet in his room where as Nathan has fixed a double door, each of width `1 1/2` feet in his room. From the closed position, if each of the single and double doors can open up to 120°, whose door takes a minimum area?
In a rectangular field which measures 15 m × 8m, cows are tied with a rope of length 3 m at four corners of the field and also at the centre. Find the area of the field where none of the cow can graze. (π = 3.14)
Three identical coins, each of diameter 6 cm are placed as shown. Find the area of the shaded region between the coins. (π = 3.14) `(sqrt(3) = 1.732)`
Using Euler’s formula, find the unknowns.
Faces | Vertices | Edges |
? | 6 | 14 |
Using Euler’s formula, find the unknowns.
Faces | Vertices | Edges |
8 | ? | 10 |
Using Euler’s formula, find the unknowns.
Faces | Verticles | Edges |
20 | 10 | ? |
Chapter 2: Measurements
Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board chapter 2 - Measurements
Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board chapter 2 (Measurements) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Mathematics Class 8th Tamil Nadu State Board solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Mathematics Class 8th Tamil Nadu State Board chapter 2 Measurements are Arc, Segment, Sector, Central Angle and the Measure of an Arc, Length of an Arc, Area of the Sector, Perimeter of a Sector, Perimeter and Area of Combined Shapes, Three Dimensional Shapes, Faces, Edges and Vertices, Nets for Building 3-d Shapes - Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism, Drawing Solids on a Flat Surface - Isometric Sketches, Cross Section of Solid Shapes, Measurements, Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles, Viewing Different Sections of a Solid.
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