# Case Study Chapter 11 Areas related to Circles Mathematics

Please refer to Case Study Chapter 11 Areas related to Circles Mathematics with answers provided below. These case study based questions are expected to come in the upcoming Class 10 Mathematics examinations. We have provided case study questions class 10 maths for all chapters on our website as per the latest examination pattern issued by CBSE, NCERT, and KVS.

## Chapter 11 Areas related to Circles Case study Questions Class 10 Maths

I. 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 sectors.
Design B: Brooch B is made with two colours — 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.

Question. The circumference of outer part (golden) is
(a) 48.49 mm
(b) 82.2 mm
(c) 72.50 mm
(d) 62.86 mm

D

Question. The difference in areas of golden and silver parts is
(a) 18π mm2
(b) 44π mm2
(c) 51π mm2
(d) 64π mm2

C

Question. A boy is playing with the brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80p mm?
(a) 2
(b) 3
(c) 4
(d) 5

C

Question. The circumference of the brooch is
(a) 28 mm
(b) 44 mm
(c) 56 mm
(d) 88 mm

D

Question. The total length of the silver wire required is
(a) 180 mm
(b) 200 mm
(c) 250 mm
(d) 280 mm

B

II . 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 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.

Question. The side of equilateral triangle is
(a) 12 √3 cm
(b) 32 √3 cm
(c) 48 cm
(d) 64 cm

B

Question. The area of square is
(a) 1264 cm2
(b) 1764 cm2
(c) 1830 cm2
(d) 1944 cm2

B

Question. Area of each circular design is
(a) 124 cm2
(b) 132 cm2
(c) 144 cm2
(d) 154 cm2

D

Question. The altitude of the equilateral triangle is
(a) 8 cm
(b) 12 cm
(c) 48 cm
(d) 52 cm

C

Question. Area of the remaining portion of the square ABCD is
(a) 378 cm2
(b) 260 cm2
(c) 340 cm2
(d) 278 cm2

A

III . Energy conservation is the effect made to reduce the consumption of energy by using less of an energy service.
Some children of a school prepared posters on ‘Save Energy’ which are shown below.

Question. What is the radius of circular region if length of poster is 18 cm and breadth is 14 cm?
(a) 14 cm
(b) 18 cm
(c) 7 cm
(d) 9 cm

C

Question. What is the area of circular region if length of poster is 18 cm and breadth is 14 cm?
(a) 154 cm2
(b) 172 cm2
(c) 196 cm2
(d) 216 cm2

A

Question. If radius of the circle is 21 cm and angle subtended by arc at centre is 60°, the length of the arc is
(a) 22 cm
(b) 28 cm
(c) 33 cm
(d) None of these.

A

Question. The area of sector formed by the arc (radius = 21 cm and angle of sector = 60°) is
(a) 124 cm2
(b) 231 cm2
(c) 285 cm2
(d) 310 cm

B

Question. The area of poster if the length and breadth of it are 18 cm and 14 cm respectively, is
(a) 155 cm2
(b) 175 cm2
(c) 195 cm2
(d) 205 cm 2