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Measurements

Class 8th Mathematics Term 1 Tamilnadu Board Solution
Exercise 2.1
  1. Area of a semicircle is ________ times the area of the circle. Choose the…
  2. Perimeter of a semicircle is ________ Choose the correct answer:A. (pi +2/2) r…
  3. If the radius of a circle is 7 m, then the area of the semicircle is _______…
  4. If the area of a circle is 144 cm^2 , then the area of its quadrant is _______…
  5. The perimeter of the quadrant of a circle of diameter 84 cm is _______ Choose…
  6. The number of quadrants in a circle is_______ Choose the correct answer:A. 1 B.…
  7. Quadrant of a circle is ______ of the circle. Choose the correct answer:A.…
  8. The central angle of a semicircle is _________ Choose the correct answer:A. 90°…
  9. The central angle of a quadrant is _______ Choose the correct answer:A. 90° B.…
  10. If the area of a semicircle is 84 cm^2 , then the area of the circle is _______…
  11. 35 cm Find the perimeter and area of semicircles whose radii are,…
  12. 10.5 cm Find the perimeter and area of semicircles whose radii are,…
  13. 6.3 m Find the perimeter and area of semicircles whose radii are,…
  14. 4.9 m Find the perimeter and area of semicircles whose radii are,…
  15. 2.8 cm Find the perimeter and area of semicircles whose diameters are,…
  16. 56 cm Find the perimeter and area of semicircles whose diameters are,…
  17. 84 cm Find the perimeter and area of semicircles whose diameters are,…
  18. 112 m Find the perimeter and area of semicircles whose diameters are,…
  19. 98 cm Calculate the perimeter and area of a quadrant of the circles whose radii…
  20. 70 cm Calculate the perimeter and area of a quadrant of the circles whose radii…
  21. 42 m Calculate the perimeter and area of a quadrant of the circles whose radii…
  22. 28 m Calculate the perimeter and area of a quadrant of the circles whose radii…
  23. Find the area of the semicircle ACB and the quadrant BOC in the given figure.…
  24. A park is in the shape of a semicircle with radius 21 m. Find the cost of…
Exercise 2.2
  1. Find the perimeter of the following figures
  2. Find the perimeter of the following figures
  3. Find the perimeter of the following figures
  4. Find the perimeter of the following figures
  5. Find the perimeter of the following figures
  6. Find the area of the following figures
  7. Find the area of the following figures
  8. a Find the area of the following figures
  9. Find the area of the following figures
  10. left arrow Find the area of the following figures
  11. Find the area of the coloured regions
  12. Find the area of the coloured regions
  13. 14cm/14cm Find the area of the coloured regions
  14. Find the area of the coloured regions
  15. a Find the area of the coloured regions
  16. s Find the area of the coloured regions
  17. In the given figure, find the area of the shaded portion if AC = 54 cm, BC = 10…
  18. A cow is tied up for grazing inside a rectangular field of dimensions 40 m × 36…
  19. A square park has each side of 100 m. At each corner of the park there is a…
  20. Find the area of the shaded region shown in the figure. The four corners are…
  21. A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A…
  22. On a square handkerchief, nine circular designs each of radius 7 cm are made.…
Exercise 2.1
Question 1.

Choose the correct answer:

Area of a semicircle is ________ times the area of the circle.
A. two

B. four

C. one-half

D. one-quarter
Answer:

As a semicircle is exact one-half of a full circle, the area of a semicircle is one-half times the area of the circle.
Question 2.

Choose the correct answer:

Perimeter of a semicircle is ________
A.

B. (π + 2) r units

C. 2r units

D. (π + 4) r units
Answer:

Perimeter of a full circle = 2πr


Thus, Perimeter of a semicircle is


= πr + 2r


= (π + 2)r units
Question 3.

Choose the correct answer:

If the radius of a circle is 7 m, then the area of the semicircle is _______
A. 77 m2

B. 44 m2

C. 88 m2

D. 154 m2
Answer:

Area of a semi-circle



= 77 m2
Question 4.

Choose the correct answer:

If the area of a circle is 144 cm2, then the area of its quadrant is _______
A. 144 cm2

B. 12 cm2

C. 72 cm2

D. 36 cm2
Answer:

Given, Area of a circle = 144 cm2


Thus, area of its quadrant is


= 36 cm2
Question 5.

Choose the correct answer:

The perimeter of the quadrant of a circle of diameter 84 cm is _______
A. 150 cm

B. 120 cm

C. 21 cm

D. 42 cm
Answer:

Given, Diameter = 84 cm


So, Radius =


= 42 cm


Perimeter of the quadrant of a circle =



= 66 + 84


= 150 cm
Question 6.

Choose the correct answer:

The number of quadrants in a circle is_______
A. 1

B. 2

C. 3

D. 4
Answer:

A quadrant is one-fourth of anything.


Hence, the number of quadrants in a circle is 4.
Question 7.

Choose the correct answer:

Quadrant of a circle is ______ of the circle.
A. one-half

B. one-fourth

C. one-third

D. two-thirds
Answer:

A quadrant of a circle is always one-fourth of the full circle .


Hence, Quadrant of a circle is one-fourth of the circle.
Question 8.

Choose the correct answer:

The central angle of a semicircle is _________
A. 90°

B. 270°

C. 180°

D. 360°
Answer:

The central angle of a semicircle is always 180°.
Question 9.

Choose the correct answer:

The central angle of a quadrant is _______
A. 90°

B. 180°

C. 270°

D. 0°
Answer:

The central angle of a quadrant is always 90°.
Question 10.

Choose the correct answer:

If the area of a semicircle is 84 cm2, then the area of the circle is _______
A. 144 cm2

B. 42 cm2

C. 168 cm2

D. 288 cm2
Answer:

Area of a semicircle = 84 cm2


Since a circle is twice of semi-circle,


Thus, Area of the circle = 2 × 84


= 168 cm2
Question 11.

Find the perimeter and area of semicircles whose radii are,

35 cm
Answer:

We know, Perimeter of semicircle = πr + 2r


And,


Area of semicircle


Radius = 35 cm


Perimeter of semicircle = πr + 2r



= 180 cm


Area of semicircle



= 1925 cm2
Question 12.

Find the perimeter and area of semicircles whose radii are,

10.5 cm
Answer:

We know, Perimeter of semicircle = πr + 2r


And,


Area of semicircle


Radius = 10.5 cm


Perimeter of semicircle = πr + 2r



= 54 cm




= 173.25 cm2
Question 13.

Find the perimeter and area of semicircles whose radii are,

6.3 m
Answer:

We know, Perimeter of semicircle = πr + 2r


And,


Area of semicircle


Radius = 6.3 cm


Perimeter of semicircle = πr + 2r



= 32.4 cm




= 62.37 cm2
Question 14.

Find the perimeter and area of semicircles whose radii are,

4.9 m
Answer:

We know, Perimeter of semicircle = πr + 2r


And,


Area of semicircle


Radius = 4.9 cm


Perimeter of semicircle = πr + 2r



= 25.2 cm




= 37.73 cm2
Question 15.

Find the perimeter and area of semicircles whose diameters are,

2.8 cm
Answer:


Diameter = 2.8 cm



= 1.4 cm


Perimeter of semicircle = πr + 2r



= 28 cm




= 3.08 cm2
Question 16.

Find the perimeter and area of semicircles whose diameters are,

56 cm
Answer:


Diameter = 56 cm



= 28 cm


Perimeter of semicircle = πr + 2r



= 144 cm




= 1232 cm2
Question 17.

Find the perimeter and area of semicircles whose diameters are,

84 cm
Answer:


Diameter = 84 cm



= 42 cm


Perimeter of semicircle = πr + 2r



= 216 cm




= 2772 cm2
Question 18.

Find the perimeter and area of semicircles whose diameters are,

112 m
Answer:


Diameter = 112 cm



= 56 cm


Perimeter of semicircle = πr + 2r



= 288 cm




= 288 cm2
Question 19.

Calculate the perimeter and area of a quadrant of the circles whose radii are,

98 cm
Answer:


Radius = 98 cm




= 50 cm




= 962.5 cm2
Question 20.

Calculate the perimeter and area of a quadrant of the circles whose radii are,

70 cm
Answer:


Radius = 70 cm




= 250 cm




= 3850 cm2
Question 21.

Calculate the perimeter and area of a quadrant of the circles whose radii are,

42 m
Answer:


Radius = 42 cm




= 150 cm




= 1386 cm2
Question 22.

Calculate the perimeter and area of a quadrant of the circles whose radii are,

28 m
Answer:


Radius = 28 cm




= 100 cm




= 616 cm2
Question 23.

Find the area of the semicircle ACB and the quadrant BOC in the given figure.
Answer:

Radius = 7 cm


So,


Area of semicircle ACB



= 77 cm2


Area of quadrant BOC



= 38.5 cm2
Question 24.

A park is in the shape of a semicircle with radius 21 m. Find the cost of fencing it at the cost of ` 5 per metre.
Answer:

Given, radius = 21 m


Cost of fencing per metre = Rs.5 per metre


Perimeter of semicircle = πr + 2r



= 108 cm


Thus, Cost of fencing per = 108 × 5


= 540 cm2
Exercise 2.2
Question 1.

Find the perimeter of the following figures
Answer:

Perimeter = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4


= 32 cm
Question 2.

Find the perimeter of the following figures
Answer:

Perimeter = 10 + 2 + 4 + 8 + 2 + 8 + 4 + 2


= 40 cm
Question 3.

Find the perimeter of the following figures
Answer:

Radius of semi-circle = 4 cm


Perimeter of semi-circle = πr


= 3.14 × 4


= 12.56 cm


Perimeter of figure = 12.56 + 4 + 4 + (6-4) + 4 + 6


= 30.56 cm
Question 4.

Find the perimeter of the following figures
Answer:

Perimeter = 7 + 13 + 13 + 7


= 40 cm
Question 5.

Find the perimeter of the following figures
Answer:

Perimeter = 10 + 10 + 10 + 6 + 13 + 10 + 13 + 6 + 10 + 10


= 98 cm
Question 6.

Find the area of the following figures
Answer:

Height of trapezium = 14-8


= 6 cm


Area of trapezium is given as, A = 1/2 × (a + b)h,


As shown below:



Where, a is the shorter side.


B is the longer side.


H is the distance between the two sides.


⇒ Area of trapezium


= 60 cm2


Area of square = 8 × 8


= 64 cm2


Area of figure = Area of trapezium + Area of square


= 60 + 64


= 124 cm2
Question 7.

Find the area of the following figures
Answer:

The figure can be re-drawn as:



Area of first triangle = 1/2 × base × height


⇒ A1 =


= 6 cm2


Area of second triangle = 1/2 × base × height


⇒ A2


= 4 cm2


Area of rectangle = length × breadth


⇒ A3 = 3 × 2


= 6 cm2


Area of square = (side)2


⇒ A4 = 3 × 3


= 9 cm2


∴ Area of figure = A1 + A2 + A3 + A4


= 6 + 4 + 6 + 9


= 25 cm2
Question 8.

Find the area of the following figures
Answer:

Diameter of semicircle = 14cm


Radius of semicircle =


= 7 cm




= 77 cm2


Area of square = (side)2 = 14 × 14


= 196 cm2


Area of figure = Area of semicircle + Area of square


= 77 + 196


= 273 cm2
Question 9.

Find the area of the following figures
Answer:

We know,



Area of two quadrants



= 25.14 cm2


Area of rectangle = length × breadth


= 6 × 4


= 24 cm2
Question 10.

Find the area of the following figures
Answer:

Radius of bigger semicircle = 2.1 m


Radius of smaller semicircles


= 1.05 m


Area of 2 smaller semicircles


∴Area of 2 smaller semicircles = πr2


Hence, area of 2 smaller semicircles


= 1.7325 m2


Area of bigger semicircle


∴Area of bigger semicircle


= 6.93 m2
Question 11.

Find the area of the coloured regions
Answer:

The figure is given below:



Area of bigger rectangle (shaded in green) = length × breadth


= 8 × 2


= 16 m2


Area of smaller rectangle (shaded in grey) = length × breadth


= 6 × 2


= 12 m2


Area of the coloured regions = Area of bigger rectangle + Area of


smaller rectangle


Area of the coloured regions = 16 + 12


= 28 m2
Question 12.

Find the area of the coloured regions
Answer:

Area of rectangle = length × breadth


= 16 × 20


= 320 m2


Area of square = side × side


= 6 × 6


= 36 m2


Area of the coloured regions = Area of rectangle + Area of square


Area of the coloured regions = 320 + 36


= 356 m2
Question 13.

Find the area of the coloured regions
Answer:

Radius of smaller semicircle


= 7 cm


Radius of bigger semicircle = 14 cm


Area of smaller semicircle



= 77 cm2




= 308 cm2


Area of the coloured regions = (Area of bigger semicircle-Area of


smaller semicircle) + Area of smaller semicircle


Area of the coloured regions = (308-77) + 77


= 308 cm2
Question 14.

Find the area of the coloured regions
Answer:

Area of square = 7 × 7


= 49 cm2


Area of semicircle



= 19.25 cm2


Area of coloured region = Area of square - 2 × Area of semicircle


= 49-2 × 19.25


= 49-38.5


= 10.5 cm2
Question 15.

Find the area of the coloured regions
Answer:

Area of rectangle = 18 × 7


= 126 cm2


Radius of bigger semicircle = 3.5 cm


Area of bigger semicircle



= 19.25 cm2


Radius of smaller semicircle


= 1.75 cm


Area of unshaded region = πr2



= 9.625 cm2


Area of coloured region = Area of bigger semicircle + ( Area of


Rectangle- Area of unshaded region)


Area of coloured region = 19.25 + (126-9.625)


= 19.25 + 116.375


= 135.625 cm2
Question 16.

Find the area of the coloured regions
Answer:




= 9.625 cm2


Area of triangle = 1/2 × base × height


= 1/2 × 3.5 × 2


= 3.5 cm2


Area of coloured region = Area of quadrant - Area of triangle


= 9.625-3.5


= 6.125 cm2
Question 17.

In the given figure, find the area of the shaded portion if AC = 54 cm, BC = 10 cm, and O is the centre of bigger circle.
Answer:

Given, AC = 54 cm


BC = 10 cm


AB = 54-10 = 44 cm


Radius of bigger circle =


= 27 cm


Area of bigger circle = πr2



= 2291.14


Radius of smaller circle =


= 22 cm


Area of smaller circle = πR2



= 1521.14


Area of the shaded portion = Area of bigger circle- Area of smaller


Circle


= 2291.14-1521.14


= 769.99 cm2


= 770 cm2
Question 18.

A cow is tied up for grazing inside a rectangular field of dimensions 40 m × 36 m in one corner of the field by a rope of length 14 m. Find the area of the field left ungrazed by the cow.
Answer:

The figure is shown below:



Area of rectangular field = 40 × 36


= 1440 m2




= 154 m2


Therefore, Area of the field left ungrazed by the cow = 1440-154


= 1286 m2
Question 19.

A square park has each side of 100 m. At each corner of the park there is a flower bed in the form of a quadrant of radius 14 m as shown in the figure. Find the area of the remaining portion of the park.
Answer:

Radius = 14 cm


One flower bed is a quadrant of the circle.


We know,



⇒ Area of one flower bed = 3.14 × 14 × 14
= 616 m2
Area of the square park = 100 × 100
= 10000 m2
Area of the four-flower bed = 4 × 616
= 2464 m2
Thus area of the remaining part = (10000-2464) m2
= 7536 m2
Question 20.

Find the area of the shaded region shown in the figure. The four corners are quadrants. At the center, there is a circle of diameter 2 cm.
Answer:

Area of square = side × side


= 4 × 4


= 16 cm2


Area of unshaded region = 4 × Area of 1 quadrant + Area of circle






= 6.28 cm2


Therefore,


Area of shaded region = Area of square- Area of


unshaded region


Area of shaded region = 16-6.28


= 9.72 cm2
Question 21.

A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semicircular portion with BC as diameter is cut off. Find the area of the remaining part.
Answer:

The figure is given below:



Diameter of semi-circle = BC = 14cm


Radius of semi–circle


= 7cm


Area of semi-circle



= 77 cm2


Area of sheet = 20 × 14 = 280 cm2


Thus, Area of remaining sheet = 280-77


= 203 cm2
Question 22.

On a square handkerchief, nine circular designs each of radius 7 cm are made. Find the area of the remaining portion of the handkerchief.
Answer:

From the figure,



Hence, it can be observed that size of side of square = 14 + 14 + 14 = 42 cm


Area of square = (side)2


= 42 × 42


= 1764 cm2


Area of each circle = πr2



= 154 cm2


Area of 9 circles = 9 × 154


= 1386 cm2


Area of unshaded region = Area of square – Area of 9 circle


= 1764 -1386


= 378 cm2