Measurements Class 8th Mathematics Term 1 Tamilnadu Board Solution

Class 8^th 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