Scroll:Measurement >> Area & Circumference of Circle >> ps (1790)


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1)  

The figure is made up of 3 semi-circles with diameter of 16 cm, 32 cm and 48 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            48 cm

cm2

cm


Answer:_______________




2)  

The figure is made up of 3 semi-circles with diameter of 52 cm, 104 cm and 156 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            156 cm

cm2

cm


Answer:_______________




3)  

The figure is made up of 3 semi-circles with diameter of 28 cm, 56 cm and 84 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            84 cm

cm2

cm


Answer:_______________




4)  

The figure is made up of 3 semi-circles with diameter of 44 cm, 88 cm and 132 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            132 cm

cm2

cm


Answer:_______________




5)  

The figure is made up of 3 semi-circles with diameter of 24 cm, 48 cm and 72 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            72 cm

cm2

cm


Answer:_______________




6)  

The figure is made up of 3 semi-circles with diameter of 32 cm, 64 cm and 96 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            96 cm

cm2

cm


Answer:_______________




7)  

The figure is made up of 3 semi-circles with diameter of 60 cm, 120 cm and 180 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            180 cm

cm2

cm


Answer:_______________




8)  

The figure is made up of 3 semi-circles with diameter of 20 cm, 40 cm and 60 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            60 cm

cm2

cm


Answer:_______________




9)  

The figure is made up of 3 semi-circles with diameter of 8 cm, 16 cm and 24 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            24 cm

cm2

cm


Answer:_______________




10)  

The figure is made up of 3 semi-circles with diameter of 36 cm, 72 cm and 108 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            108 cm

cm2

cm


Answer:_______________




 

1)  

The figure is made up of 3 semi-circles with diameter of 16 cm, 32 cm and 48 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            48 cm

Answer: 402 cm2

Answer: 75 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 48 ÷ 2

                                                      = 24 cm

Step 2: Radius of medium semi-circe → 32 ÷ 2

                                                            = 16 cm

Step 3: Radius of small semi-circle → 48 ÷ 2

                                                         = 8 cm

Step 4: Area of big semi circle → 12 x π x 24 cm x 24 cm

                                                 = 904.896 cm2

Step 5: Area of medium semi circle → 12 x π x 16 cm x 16 cm

                                                         = 402.176 cm2

Step 6: Area of small circle → 12 x π x 8 cm x 8 cm

                                            = 100.544 cm2

Step 7: Area of the shaded part → 904.896 cm2 - 402.176 cm2 - 100.544 cm2

                                                    = 402.176 cm2

                                                    ≈ 402 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 48 cm

                                                                 = 37.704 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 32 cm

                                                                         = 25.136 cm

Step 10: Circumference of small semi circle →1 2 x π x 16 cm

                                                                     = 12.568 cm

Step 11: Perimeter of shaded part → 37.704 cm + 25.136 cm + 12.568 cm

                                                       = 75.408 cm

                                                       ≈ 75 cm



2)  

The figure is made up of 3 semi-circles with diameter of 52 cm, 104 cm and 156 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            156 cm

Answer: 4248 cm2

Answer: 245 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 156 ÷ 2

                                                      = 78 cm

Step 2: Radius of medium semi-circe → 104 ÷ 2

                                                            = 52 cm

Step 3: Radius of small semi-circle → 156 ÷ 2

                                                         = 26 cm

Step 4: Area of big semi circle → 12 x π x 78 cm x 78 cm

                                                 = 9557.964 cm2

Step 5: Area of medium semi circle → 12 x π x 52 cm x 52 cm

                                                         = 4247.984 cm2

Step 6: Area of small circle → 12 x π x 26 cm x 26 cm

                                            = 1061.996 cm2

Step 7: Area of the shaded part → 9557.964 cm2 - 4247.984 cm2 - 1061.996 cm2

                                                    = 4247.984 cm2

                                                    ≈ 4248 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 156 cm

                                                                 = 122.538 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 104 cm

                                                                         = 81.692 cm

Step 10: Circumference of small semi circle →1 2 x π x 52 cm

                                                                     = 40.846 cm

Step 11: Perimeter of shaded part → 122.538 cm + 81.692 cm + 40.846 cm

                                                       = 245.076 cm

                                                       ≈ 245 cm



3)  

The figure is made up of 3 semi-circles with diameter of 28 cm, 56 cm and 84 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            84 cm

Answer: 1232 cm2

Answer: 132 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 84 ÷ 2

                                                      = 42 cm

Step 2: Radius of medium semi-circe → 56 ÷ 2

                                                            = 28 cm

Step 3: Radius of small semi-circle → 84 ÷ 2

                                                         = 14 cm

Step 4: Area of big semi circle → 12 x π x 42 cm x 42 cm

                                                 = 2771.244 cm2

Step 5: Area of medium semi circle → 12 x π x 28 cm x 28 cm

                                                         = 1231.664 cm2

Step 6: Area of small circle → 12 x π x 14 cm x 14 cm

                                            = 307.916 cm2

Step 7: Area of the shaded part → 2771.244 cm2 - 1231.664 cm2 - 307.916 cm2

                                                    = 1231.664 cm2

                                                    ≈ 1232 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 84 cm

                                                                 = 65.982 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 56 cm

                                                                         = 43.988 cm

Step 10: Circumference of small semi circle →1 2 x π x 28 cm

                                                                     = 21.994 cm

Step 11: Perimeter of shaded part → 65.982 cm + 43.988 cm + 21.994 cm

                                                       = 131.964 cm

                                                       ≈ 132 cm



4)  

The figure is made up of 3 semi-circles with diameter of 44 cm, 88 cm and 132 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            132 cm

Answer: 3041 cm2

Answer: 207 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 132 ÷ 2

                                                      = 66 cm

Step 2: Radius of medium semi-circe → 88 ÷ 2

                                                            = 44 cm

Step 3: Radius of small semi-circle → 132 ÷ 2

                                                         = 22 cm

Step 4: Area of big semi circle → 12 x π x 66 cm x 66 cm

                                                 = 6843.276 cm2

Step 5: Area of medium semi circle → 12 x π x 44 cm x 44 cm

                                                         = 3041.456 cm2

Step 6: Area of small circle → 12 x π x 22 cm x 22 cm

                                            = 760.364 cm2

Step 7: Area of the shaded part → 6843.276 cm2 - 3041.456 cm2 - 760.364 cm2

                                                    = 3041.456 cm2

                                                    ≈ 3041 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 132 cm

                                                                 = 103.686 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 88 cm

                                                                         = 69.124 cm

Step 10: Circumference of small semi circle →1 2 x π x 44 cm

                                                                     = 34.562 cm

Step 11: Perimeter of shaded part → 103.686 cm + 69.124 cm + 34.562 cm

                                                       = 207.372 cm

                                                       ≈ 207 cm



5)  

The figure is made up of 3 semi-circles with diameter of 24 cm, 48 cm and 72 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            72 cm

Answer: 905 cm2

Answer: 113 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 72 ÷ 2

                                                      = 36 cm

Step 2: Radius of medium semi-circe → 48 ÷ 2

                                                            = 24 cm

Step 3: Radius of small semi-circle → 72 ÷ 2

                                                         = 12 cm

Step 4: Area of big semi circle → 12 x π x 36 cm x 36 cm

                                                 = 2036.016 cm2

Step 5: Area of medium semi circle → 12 x π x 24 cm x 24 cm

                                                         = 904.896 cm2

Step 6: Area of small circle → 12 x π x 12 cm x 12 cm

                                            = 226.224 cm2

Step 7: Area of the shaded part → 2036.016 cm2 - 904.896 cm2 - 226.224 cm2

                                                    = 904.896 cm2

                                                    ≈ 905 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 72 cm

                                                                 = 56.556 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 48 cm

                                                                         = 37.704 cm

Step 10: Circumference of small semi circle →1 2 x π x 24 cm

                                                                     = 18.852 cm

Step 11: Perimeter of shaded part → 56.556 cm + 37.704 cm + 18.852 cm

                                                       = 113.112 cm

                                                       ≈ 113 cm



6)  

The figure is made up of 3 semi-circles with diameter of 32 cm, 64 cm and 96 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            96 cm

Answer: 1609 cm2

Answer: 151 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 96 ÷ 2

                                                      = 48 cm

Step 2: Radius of medium semi-circe → 64 ÷ 2

                                                            = 32 cm

Step 3: Radius of small semi-circle → 96 ÷ 2

                                                         = 16 cm

Step 4: Area of big semi circle → 12 x π x 48 cm x 48 cm

                                                 = 3619.584 cm2

Step 5: Area of medium semi circle → 12 x π x 32 cm x 32 cm

                                                         = 1608.704 cm2

Step 6: Area of small circle → 12 x π x 16 cm x 16 cm

                                            = 402.176 cm2

Step 7: Area of the shaded part → 3619.584 cm2 - 1608.704 cm2 - 402.176 cm2

                                                    = 1608.704 cm2

                                                    ≈ 1609 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 96 cm

                                                                 = 75.408 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 64 cm

                                                                         = 50.272 cm

Step 10: Circumference of small semi circle →1 2 x π x 32 cm

                                                                     = 25.136 cm

Step 11: Perimeter of shaded part → 75.408 cm + 50.272 cm + 25.136 cm

                                                       = 150.816 cm

                                                       ≈ 151 cm



7)  

The figure is made up of 3 semi-circles with diameter of 60 cm, 120 cm and 180 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            180 cm

Answer: 5656 cm2

Answer: 283 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 180 ÷ 2

                                                      = 90 cm

Step 2: Radius of medium semi-circe → 120 ÷ 2

                                                            = 60 cm

Step 3: Radius of small semi-circle → 180 ÷ 2

                                                         = 30 cm

Step 4: Area of big semi circle → 12 x π x 90 cm x 90 cm

                                                 = 12725.100 cm2

Step 5: Area of medium semi circle → 12 x π x 60 cm x 60 cm

                                                         = 5655.600 cm2

Step 6: Area of small circle → 12 x π x 30 cm x 30 cm

                                            = 1413.900 cm2

Step 7: Area of the shaded part → 12725.100 cm2 - 5655.600 cm2 - 1413.900 cm2

                                                    = 5655.600 cm2

                                                    ≈ 5656 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 180 cm

                                                                 = 141.390 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 120 cm

                                                                         = 94.260 cm

Step 10: Circumference of small semi circle →1 2 x π x 60 cm

                                                                     = 47.130 cm

Step 11: Perimeter of shaded part → 141.390 cm + 94.260 cm + 47.130 cm

                                                       = 282.780 cm

                                                       ≈ 283 cm



8)  

The figure is made up of 3 semi-circles with diameter of 20 cm, 40 cm and 60 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            60 cm

Answer: 628 cm2

Answer: 94 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 60 ÷ 2

                                                      = 30 cm

Step 2: Radius of medium semi-circe → 40 ÷ 2

                                                            = 20 cm

Step 3: Radius of small semi-circle → 60 ÷ 2

                                                         = 10 cm

Step 4: Area of big semi circle → 12 x π x 30 cm x 30 cm

                                                 = 1413.900 cm2

Step 5: Area of medium semi circle → 12 x π x 20 cm x 20 cm

                                                         = 628.400 cm2

Step 6: Area of small circle → 12 x π x 10 cm x 10 cm

                                            = 157.100 cm2

Step 7: Area of the shaded part → 1413.900 cm2 - 628.400 cm2 - 157.100 cm2

                                                    = 628.400 cm2

                                                    ≈ 628 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 60 cm

                                                                 = 47.130 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 40 cm

                                                                         = 31.420 cm

Step 10: Circumference of small semi circle →1 2 x π x 20 cm

                                                                     = 15.710 cm

Step 11: Perimeter of shaded part → 47.130 cm + 31.420 cm + 15.710 cm

                                                       = 94.260 cm

                                                       ≈ 94 cm



9)  

The figure is made up of 3 semi-circles with diameter of 8 cm, 16 cm and 24 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            24 cm

Answer: 101 cm2

Answer: 38 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 24 ÷ 2

                                                      = 12 cm

Step 2: Radius of medium semi-circe → 16 ÷ 2

                                                            = 8 cm

Step 3: Radius of small semi-circle → 24 ÷ 2

                                                         = 4 cm

Step 4: Area of big semi circle → 12 x π x 12 cm x 12 cm

                                                 = 226.224 cm2

Step 5: Area of medium semi circle → 12 x π x 8 cm x 8 cm

                                                         = 100.544 cm2

Step 6: Area of small circle → 12 x π x 4 cm x 4 cm

                                            = 25.136 cm2

Step 7: Area of the shaded part → 226.224 cm2 - 100.544 cm2 - 25.136 cm2

                                                    = 100.544 cm2

                                                    ≈ 101 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 24 cm

                                                                 = 18.852 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 16 cm

                                                                         = 12.568 cm

Step 10: Circumference of small semi circle →1 2 x π x 8 cm

                                                                     = 6.284 cm

Step 11: Perimeter of shaded part → 18.852 cm + 12.568 cm + 6.284 cm

                                                       = 37.704 cm

                                                       ≈ 38 cm



10)  

The figure is made up of 3 semi-circles with diameter of 36 cm, 72 cm and 108 cm respectively.

Find the area and the perimeter of the shaded part, rounding off your answers to the nearest whole number. 

π = 3.142

                            108 cm

Answer: 2036 cm2

Answer: 170 cm


SOLUTION 1 :

Step 1: Radius of big semi-circle 108 ÷ 2

                                                      = 54 cm

Step 2: Radius of medium semi-circe → 72 ÷ 2

                                                            = 36 cm

Step 3: Radius of small semi-circle → 108 ÷ 2

                                                         = 18 cm

Step 4: Area of big semi circle → 12 x π x 54 cm x 54 cm

                                                 = 4581.036 cm2

Step 5: Area of medium semi circle → 12 x π x 36 cm x 36 cm

                                                         = 2036.016 cm2

Step 6: Area of small circle → 12 x π x 18 cm x 18 cm

                                            = 509.004 cm2

Step 7: Area of the shaded part → 4581.036 cm2 - 2036.016 cm2 - 509.004 cm2

                                                    = 2036.016 cm2

                                                    ≈ 2036 cm2

Step 8: Circumference of big semi circle → 1 2 x π x 108 cm

                                                                 = 84.834 cm

Step 9: Circumference of medium semi circle → 1 2 x π x 72 cm

                                                                         = 56.556 cm

Step 10: Circumference of small semi circle →1 2 x π x 36 cm

                                                                     = 28.278 cm

Step 11: Perimeter of shaded part → 84.834 cm + 56.556 cm + 28.278 cm

                                                       = 169.668 cm

                                                       ≈ 170 cm