Scroll:Measurement >> Area & Perimeter of Composite Figure >> ps (2890)

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For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

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1)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 42 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

π cm


Answer:_______________




2)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 144 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

π cm2


Answer:_______________




3)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 34 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

π cm


Answer:_______________




4)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 96 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

π cm2


Answer:_______________




5)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 24 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

π cm


Answer:_______________




6)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 136 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

π cm2


Answer:_______________




7)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 20 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

π cm


Answer:_______________




8)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 120 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

π cm2


Answer:_______________




9)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 30 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

π cm


Answer:_______________




10)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 88 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

π cm2


Answer:_______________




 

1)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 42 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

Answer: 294 π cm


SOLUTION 1 :

Step 1: Radius of small circle → 42 cm ÷ 2

                                                = 21 cm

Step 2: Radius of big circle → 42 cm + 42 cm

                                            = 63 cm

Step 3: Circumference of 2 small circles → 2 x 2 x π x 21 cm  

                                                                = 84 π cm

Step 4: Circumference of medium circle →  2 x π x 42 cm

                                                                = 84 π cm

Step 5: Circumference of big circle → 2 x π x 63 cm

                                                        = 126 π cm

Step 6: Circumference of shaded part → 84 π cm + 84 π cm + 126 π cm

                                                             = 294 π cm



2)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 144 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

Answer: 2592 π cm2


SOLUTION 1 :

Step 1: Radius of big circle → 144 cm ÷ 2

                                            = 72 cm

Step 2: Area of big circle → π r2 = π x 722

                                                    = 5184 π cm2

Step 3: Radius of medium circle → 72 cm ÷ 2

                                                   = 36 cm

Step 4: Area of medium circle → π r2 = π x 362

                                                           = 1296 π cm2

Step 5: Radius of small circle → 36 cm ÷ 2

                                               = 18 cm

Step 6: Area of small circle → π r2 = π x 182

                                                       = 324 π cm2

Step 7: Area of  4 small circles → 4 x 324 π cm2

                                                 = 1296 π cm2

Step 8: Shaded area → 5184 π cm2 - 1296 π cm2 - 1296 π cm2

                                  = 2592 π cm2



3)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 34 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

Answer: 238 π cm


SOLUTION 1 :

Step 1: Radius of small circle → 34 cm ÷ 2

                                                = 17 cm

Step 2: Radius of big circle → 34 cm + 34 cm

                                            = 51 cm

Step 3: Circumference of 2 small circles → 2 x 2 x π x 17 cm  

                                                                = 68 π cm

Step 4: Circumference of medium circle →  2 x π x 34 cm

                                                                = 68 π cm

Step 5: Circumference of big circle → 2 x π x 51 cm

                                                        = 102 π cm

Step 6: Circumference of shaded part → 68 π cm + 68 π cm + 102 π cm

                                                             = 238 π cm



4)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 96 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

Answer: 1152 π cm2


SOLUTION 1 :

Step 1: Radius of big circle → 96 cm ÷ 2

                                            = 48 cm

Step 2: Area of big circle → π r2 = π x 482

                                                    = 2304 π cm2

Step 3: Radius of medium circle → 48 cm ÷ 2

                                                   = 24 cm

Step 4: Area of medium circle → π r2 = π x 242

                                                           = 576 π cm2

Step 5: Radius of small circle → 24 cm ÷ 2

                                               = 12 cm

Step 6: Area of small circle → π r2 = π x 122

                                                       = 144 π cm2

Step 7: Area of  4 small circles → 4 x 144 π cm2

                                                 = 576 π cm2

Step 8: Shaded area → 2304 π cm2 - 576 π cm2 - 576 π cm2

                                  = 1152 π cm2



5)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 24 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

Answer: 168 π cm


SOLUTION 1 :

Step 1: Radius of small circle → 24 cm ÷ 2

                                                = 12 cm

Step 2: Radius of big circle → 24 cm + 24 cm

                                            = 36 cm

Step 3: Circumference of 2 small circles → 2 x 2 x π x 12 cm  

                                                                = 48 π cm

Step 4: Circumference of medium circle →  2 x π x 24 cm

                                                                = 48 π cm

Step 5: Circumference of big circle → 2 x π x 36 cm

                                                        = 72 π cm

Step 6: Circumference of shaded part → 48 π cm + 48 π cm + 72 π cm

                                                             = 168 π cm



6)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 136 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

Answer: 2312 π cm2


SOLUTION 1 :

Step 1: Radius of big circle → 136 cm ÷ 2

                                            = 68 cm

Step 2: Area of big circle → π r2 = π x 682

                                                    = 4624 π cm2

Step 3: Radius of medium circle → 68 cm ÷ 2

                                                   = 34 cm

Step 4: Area of medium circle → π r2 = π x 342

                                                           = 1156 π cm2

Step 5: Radius of small circle → 34 cm ÷ 2

                                               = 17 cm

Step 6: Area of small circle → π r2 = π x 172

                                                       = 289 π cm2

Step 7: Area of  4 small circles → 4 x 289 π cm2

                                                 = 1156 π cm2

Step 8: Shaded area → 4624 π cm2 - 1156 π cm2 - 1156 π cm2

                                  = 2312 π cm2



7)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 20 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

Answer: 140 π cm


SOLUTION 1 :

Step 1: Radius of small circle → 20 cm ÷ 2

                                                = 10 cm

Step 2: Radius of big circle → 20 cm + 20 cm

                                            = 30 cm

Step 3: Circumference of 2 small circles → 2 x 2 x π x 10 cm  

                                                                = 40 π cm

Step 4: Circumference of medium circle →  2 x π x 20 cm

                                                                = 40 π cm

Step 5: Circumference of big circle → 2 x π x 30 cm

                                                        = 60 π cm

Step 6: Circumference of shaded part → 40 π cm + 40 π cm + 60 π cm

                                                             = 140 π cm



8)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 120 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

Answer: 1800 π cm2


SOLUTION 1 :

Step 1: Radius of big circle → 120 cm ÷ 2

                                            = 60 cm

Step 2: Area of big circle → π r2 = π x 602

                                                    = 3600 π cm2

Step 3: Radius of medium circle → 60 cm ÷ 2

                                                   = 30 cm

Step 4: Area of medium circle → π r2 = π x 302

                                                           = 900 π cm2

Step 5: Radius of small circle → 30 cm ÷ 2

                                               = 15 cm

Step 6: Area of small circle → π r2 = π x 152

                                                       = 225 π cm2

Step 7: Area of  4 small circles → 4 x 225 π cm2

                                                 = 900 π cm2

Step 8: Shaded area → 3600 π cm2 - 900 π cm2 - 900 π cm2

                                  = 1800 π cm2



9)  

The figure below is made up of one big circle, one medium circle and two identical small circles. The radius of the medium circle is 30 cm. The ratio of the radius of the small circle to the radius of the medium circle is 1 : 2.

What is the perimeter of the shaded part in the figure Give your answer in terms of π .

Answer: 210 π cm


SOLUTION 1 :

Step 1: Radius of small circle → 30 cm ÷ 2

                                                = 15 cm

Step 2: Radius of big circle → 30 cm + 30 cm

                                            = 45 cm

Step 3: Circumference of 2 small circles → 2 x 2 x π x 15 cm  

                                                                = 60 π cm

Step 4: Circumference of medium circle →  2 x π x 30 cm

                                                                = 60 π cm

Step 5: Circumference of big circle → 2 x π x 45 cm

                                                        = 90 π cm

Step 6: Circumference of shaded part → 60 π cm + 60 π cm + 90 π cm

                                                             = 210 π cm



10)  

The figure below shows four identical small circles, one medium circle and one big circle. The diameter of the big circle is 88 cm. The radius of the medium circle is twice the radius of each small circle.

Find the shaded area in terms of π . 

Answer: 968 π cm2


SOLUTION 1 :

Step 1: Radius of big circle → 88 cm ÷ 2

                                            = 44 cm

Step 2: Area of big circle → π r2 = π x 442

                                                    = 1936 π cm2

Step 3: Radius of medium circle → 44 cm ÷ 2

                                                   = 22 cm

Step 4: Area of medium circle → π r2 = π x 222

                                                           = 484 π cm2

Step 5: Radius of small circle → 22 cm ÷ 2

                                               = 11 cm

Step 6: Area of small circle → π r2 = π x 112

                                                       = 121 π cm2

Step 7: Area of  4 small circles → 4 x 121 π cm2

                                                 = 484 π cm2

Step 8: Shaded area → 1936 π cm2 - 484 π cm2 - 484 π cm2

                                  = 968 π cm2