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Case Based Questions Test: Areas Related to Circles - 1 - Class 10 MCQ


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10 Questions MCQ Test Online MCQ Tests for Class 10 - Case Based Questions Test: Areas Related to Circles - 1

Case Based Questions Test: Areas Related to Circles - 1 for Class 10 2024 is part of Online MCQ Tests for Class 10 preparation. The Case Based Questions Test: Areas Related to Circles - 1 questions and answers have been prepared according to the Class 10 exam syllabus.The Case Based Questions Test: Areas Related to Circles - 1 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Case Based Questions Test: Areas Related to Circles - 1 below.
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Case Based Questions Test: Areas Related to Circles - 1 - Question 1

Read the following text and answer the following question on the basis of the same:

A horse is tied to a peg at one corner of a square shaped grass field of sides 15 m by means of a 5 m long rope (see the given figure).

What is the area of the grass field?

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 1
Area of square = (side)2

= 15 × 15

= 225 m2

Case Based Questions Test: Areas Related to Circles - 1 - Question 2

Read the following text and answer the following question on the basis of the same:

A horse is tied to a peg at one corner of a square shaped grass field of sides 15 m by means of a 5 m long rope (see the given figure).

The grazing area if the rope were 10 m long instead of 5 m.

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 2
Area that can be grazed by the horse when length of rope is 10 m long

Case Based Questions Test: Areas Related to Circles - 1 - Question 3

Read the following text and answer the following question on the basis of the same:

A horse is tied to a peg at one corner of a square shaped grass field of sides 15 m by means of a 5 m long rope (see the given figure).

The given problem is based on which concept?

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 3
Any chord AB divides circle into two parts.

The bigger part is known as major segment and smaller one is called minor segment.

Area of major segment OAQB = πr2 - area of minor segment APB.

Area of segment of a circle = Area of the corresponding sector - Area of the corresponding triangle.

Case Based Questions Test: Areas Related to Circles - 1 - Question 4

Read the following text and answer the following question on the basis of the same:

In a workshop, brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the given figure.

What is the circumference of the brooch?

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 4
Circumference of brooch = 2πr

Case Based Questions Test: Areas Related to Circles - 1 - Question 5

Read the following text and answer the following question on the basis of the same:

In a workshop, brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the given figure.

What is the area of the each sector of the brooch?

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 5
It can be observed from the figure that an angle of each 10 sectors of the circle is subtending at the centre of the circle.

∴ Area of each sector

Case Based Questions Test: Areas Related to Circles - 1 - Question 6

Read the following text and answer the following question on the basis of the same:

Areas Related to Circles

Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend, who is a partner in the competition, suggests two designs given below.

Observe these carefully.

Design I: This design is made with a circle of radius 32 cm leaving equilateral triangle ABC in the middle as shown in the given figure.

Design II: This Pookalam is made with 9 circular design each of radius 7 cm.

Refer Design I:The side of equilateral triangle is

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 6
Let centre of circle be O.

Join OA, OB and OC

Now,

OA = OB = OC = Radius of circle = 32 sm

Let’s consider △OBC

Let’s draw OM ⊥ BC

By symmetry,

In right triangle △OMB

16√3 = BM

Thus,

BC = 2 x BM

= 2 x 16√3

= 32√3

Case Based Questions Test: Areas Related to Circles - 1 - Question 7

Read the following text and answer the following question on the basis of the same:

Areas Related to Circles Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend, who is a partner in the competition, suggests two designs given below.

Observe these carefully.

Design I: This design is made with a circle of radius 32 cm leaving equilateral triangle ABC in the middle as shown in the given figure.

Design II: This Pookalam is made with 9 circular design each of radius 7 cm.

Refer Design II:The area of square is

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 7
radius = 7 cm

diameter = 2 × 7 cm

= 14 cm

side of square = 14 cm + 14 cm + 14 cm

= 42 cm.

Area of square = side2

= (42 cm)2

= 1764 cm2

Case Based Questions Test: Areas Related to Circles - 1 - Question 8

Read the following text and answer the following question on the basis of the same:

Areas Related to Circles Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend, who is a partner in the competition, suggests two designs given below.

Observe these carefully.

Design I: This design is made with a circle of radius 32 cm leaving equilateral triangle ABC in the middle as shown in the given figure.

Design II: This Pookalam is made with 9 circular design each of radius 7 cm.

Refer Design II:Area of the remaining portion of the square ABCD
Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 8
Area of 9 circular design

= 9 × πr2

= 1386 cm2

Area of square = 1764 cm2

Area of remaining portion of square ABCD

= Area of square – Area of 9

circular design

= 1764 cm2 – 1386 cm2

= 378 cm2

Case Based Questions Test: Areas Related to Circles - 1 - Question 9

Read the following text and answer the following question on the basis of the same:

A Brooch

A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully.

Design A: Brooch A is made with silver wire in the form of a circle with diameter 28 mm. The wire used for making 4 diameters which divide the circle into 8 equal parts.

Design B: Brooch b is made two colours i.e. Gold and silver. Outer part is made with Gold. The circumference of silver part is 44 mm and the gold part is 3 mm wide everywhere.

Refer to Design AThe area of each sector of the brooch is
Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 9
Area of each sector of Brooch

= 1/8 x Area of Brooch

Case Based Questions Test: Areas Related to Circles - 1 - Question 10

Read the following text and answer the following question on the basis of the same:

A Brooch

A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully.

Design A: Brooch A is made with silver wire in the form of a circle with diameter 28 mm. The wire used for making 4 diameters which divide the circle into 8 equal parts.

Design B: Brooch b is made two colours i.e. Gold and silver. Outer part is made with Gold. The circumference of silver part is 44 mm and the gold part is 3 mm wide everywhere.

Refer to Design BThe difference of areas of golden and silver parts is

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 1 - Question 10
Difference between areas of golden and silver part

= Area of silver - Area of golden

= Area of circle of radius 10mm - Area of circle of radius 7mm

= π(10)2 - π(7)2

= 100π - 49π

= 51π

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