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