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

Case Based Questions Test: Areas Related to Circles - 2 for Class 10 2024 is part of Online MCQ Tests for Class 10 preparation. The Case Based Questions Test: Areas Related to Circles - 2 questions and answers have been prepared according to the Class 10 exam syllabus.The Case Based Questions Test: Areas Related to Circles - 2 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 - 2 below.
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Case Based Questions Test: Areas Related to Circles - 2 - 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).

The area of that part of the field in which the horse can graze.

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 1
From the figure, it can be observed that the horse can graze a sector of 90° in a circle of 5 m radius.

Area that can be grazed by horse

= Area of sector

Case Based Questions Test: Areas Related to Circles - 2 - 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 increase in 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 - 2 - Question 2
Increase in grazing area

= (78.5 – 19.625) m2

= 58.875 m2

Case Based Questions Test: Areas Related to Circles - 2 - Question 3

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 radius of the circle?

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 3
Radius of circle = Diameter/2

= 35/2 mm

Case Based Questions Test: Areas Related to Circles - 2 - 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 total length of silver wire required?

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 4
Length of wire required

= 110 + 5 × 35

= 110 + 175

= 285 mm.

Case Based Questions Test: Areas Related to Circles - 2 - 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.

The given problem is based on which mathematical concept?

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 5
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 - 2 - 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 altitude of the equilateral triangle is

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 6
Altitude of equilateral triangle

= AM

= OA + OM

= 32 + OM

Let’s find OM

Let’s take △OMB

In right triangle △OMB

1/2 = OM/32

32/2 = OM

16 = OM

OM = 16

Thus,

Altitude of equilateral triangle = 32 + OM = 32 + 16 = 48 cm

Case Based Questions Test: Areas Related to Circles - 2 - 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:Area of each circular design is

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 7
radius = 7 cm

Area of each circular design

= πr2

= 22/7 x 7 x 7

= 154 cm2

Case Based Questions Test: Areas Related to Circles - 2 - Question 8

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

A BroochA 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 total length of silver wire required is
Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 8
Diameter = 28 mm

radius = 14 mm

Total length of wire = length of 4 diameter + circumference of circle.

= 4 × 28 + 2πr

112 + 2 x 22/7 x 14

= 112 + 88

= 200 mm

Case Based Questions Test: Areas Related to Circles - 2 - 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 BThe circumference of outer part (golden) is

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 9
Circumference of silver part is 44 mm

2πr = 44

R = 7 mm

Thus,

Radius of golden + silver part = 7 + 3 = 10 mm

Now,

Circumference of Golden part

= 2π x Radius of (golden + silver) part

= 2 x 3.143 x 10

= 6.286 x 10

= 62.86 mm

Case Based Questions Test: Areas Related to Circles - 2 - 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 BA boy is playing with brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80 mm?

Detailed Solution for Case Based Questions Test: Areas Related to Circles - 2 - Question 10
Circumference of silver part of Brooch

= 44 cm

2πr = 44 mm

2 x 22/7 x r = 44

r = 7 mm.

radius of whole Brooch = 7mm + 8 mm

= 10 mm.

Circumference of outer edge

= 2πr

2 x 22/7 x 10

= 440/7 mm

let the number of revolutions = n

Now, According to question,

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