Sasi Math (Revised for 1024)

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

Written Instructions:

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..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

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

Answer:_______________

The figure is made up of 3 semi-circles with diameter of 12 cm, 24 cm and 36 cm respectively.

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

π = 3.142

36 cm

cm²

Answer:_______________

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

Answer:_______________

The figure is made up of 3 semi-circles with diameter of 48 cm, 96 cm and 144 cm respectively.

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

π = 3.142

144 cm

cm²

Answer:_______________

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

Answer:_______________

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

Answer:_______________

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

Answer:_______________

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

Answer:_______________

The figure is made up of 3 semi-circles with diameter of 64 cm, 128 cm and 192 cm respectively.

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

π = 3.142

192 cm

cm²

Answer:_______________

10)

The figure is made up of 3 semi-circles with diameter of 56 cm, 112 cm and 168 cm respectively.

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

π = 3.142

168 cm

cm²

Answer:_______________

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 → $\frac{1}{2}$ x π x 90 cm x 90 cm

= 12725.100 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 60 cm x 60 cm

= 5655.600 cm²

Step 6: Area of small circle → $\frac{1}{2}$ 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 → $\frac{1}{2}$ x π x 180 cm

= 141.390 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 120 cm

= 94.260 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ 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

The figure is made up of 3 semi-circles with diameter of 12 cm, 24 cm and 36 cm respectively.

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

π = 3.142

36 cm

Answer: 226 cm²

Answer: 57 cm

SOLUTION 1 :

Step 1: Radius of big semi-circle → 36 ÷ 2

= 18 cm

Step 2: Radius of medium semi-circe → 24 ÷ 2

= 12 cm

Step 3: Radius of small semi-circle → 36 ÷ 2

= 6 cm

Step 4: Area of big semi circle → $\frac{1}{2}$ x π x 18 cm x 18 cm

= 509.004 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 12 cm x 12 cm

= 226.224 cm²

Step 6: Area of small circle → $\frac{1}{2}$ x π x 6 cm x 6 cm

= 56.556 cm²

Step 7: Area of the shaded part → 509.004 cm² - 226.224 cm² - 56.556 cm²

= 226.224 cm²

≈ 226 cm²

Step 8: Circumference of big semi circle → $\frac{1}{2}$ x π x 36 cm

= 28.278 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 24 cm

= 18.852 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ x π x 12 cm

= 9.426 cm

Step 11: Perimeter of shaded part → 28.278 cm + 18.852 cm + 9.426 cm

= 56.556 cm

≈ 57 cm

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 → $\frac{1}{2}$ x π x 30 cm x 30 cm

= 1413.900 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 20 cm x 20 cm

= 628.400 cm²

Step 6: Area of small circle → $\frac{1}{2}$ 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 → $\frac{1}{2}$ x π x 60 cm

= 47.130 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 40 cm

= 31.420 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ 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

The figure is made up of 3 semi-circles with diameter of 48 cm, 96 cm and 144 cm respectively.

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

π = 3.142

144 cm

Answer: 3620 cm²

Answer: 226 cm

SOLUTION 1 :

Step 1: Radius of big semi-circle → 144 ÷ 2

= 72 cm

Step 2: Radius of medium semi-circe → 96 ÷ 2

= 48 cm

Step 3: Radius of small semi-circle → 144 ÷ 2

= 24 cm

Step 4: Area of big semi circle → $\frac{1}{2}$ x π x 72 cm x 72 cm

= 8144.064 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 48 cm x 48 cm

= 3619.584 cm²

Step 6: Area of small circle → $\frac{1}{2}$ x π x 24 cm x 24 cm

= 904.896 cm²

Step 7: Area of the shaded part → 8144.064 cm² - 3619.584 cm² - 904.896 cm²

= 3619.584 cm²

≈ 3620 cm²

Step 8: Circumference of big semi circle → $\frac{1}{2}$ x π x 144 cm

= 113.112 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 96 cm

= 75.408 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ x π x 48 cm

= 37.704 cm

Step 11: Perimeter of shaded part → 113.112 cm + 75.408 cm + 37.704 cm

= 226.224 cm

≈ 226 cm

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 → $\frac{1}{2}$ x π x 24 cm x 24 cm

= 904.896 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 16 cm x 16 cm

= 402.176 cm²

Step 6: Area of small circle → $\frac{1}{2}$ 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 → $\frac{1}{2}$ x π x 48 cm

= 37.704 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 32 cm

= 25.136 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ 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

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 → $\frac{1}{2}$ x π x 36 cm x 36 cm

= 2036.016 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 24 cm x 24 cm

= 904.896 cm²

Step 6: Area of small circle → $\frac{1}{2}$ 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 → $\frac{1}{2}$ x π x 72 cm

= 56.556 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 48 cm

= 37.704 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ 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

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 → $\frac{1}{2}$ x π x 12 cm x 12 cm

= 226.224 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 8 cm x 8 cm

= 100.544 cm²

Step 6: Area of small circle → $\frac{1}{2}$ 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 → $\frac{1}{2}$ x π x 24 cm

= 18.852 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 16 cm

= 12.568 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ 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

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 → $\frac{1}{2}$ x π x 54 cm x 54 cm

= 4581.036 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 36 cm x 36 cm

= 2036.016 cm²

Step 6: Area of small circle → $\frac{1}{2}$ 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 → $\frac{1}{2}$ x π x 108 cm

= 84.834 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 72 cm

= 56.556 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ 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

The figure is made up of 3 semi-circles with diameter of 64 cm, 128 cm and 192 cm respectively.

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

π = 3.142

192 cm

Answer: 6435 cm²

Answer: 302 cm

SOLUTION 1 :

Step 1: Radius of big semi-circle → 192 ÷ 2

= 96 cm

Step 2: Radius of medium semi-circe → 128 ÷ 2

= 64 cm

Step 3: Radius of small semi-circle → 192 ÷ 2

= 32 cm

Step 4: Area of big semi circle → $\frac{1}{2}$ x π x 96 cm x 96 cm

= 14478.336 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 64 cm x 64 cm

= 6434.816 cm²

Step 6: Area of small circle → $\frac{1}{2}$ x π x 32 cm x 32 cm

= 1608.704 cm²

Step 7: Area of the shaded part → 14478.336 cm² - 6434.816 cm² - 1608.704 cm²

= 6434.816 cm²

≈ 6435 cm²

Step 8: Circumference of big semi circle → $\frac{1}{2}$ x π x 192 cm

= 150.816 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 128 cm

= 100.544 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ x π x 64 cm

= 50.272 cm

Step 11: Perimeter of shaded part → 150.816 cm + 100.544 cm + 50.272 cm

= 301.632 cm

≈ 302 cm

10)

The figure is made up of 3 semi-circles with diameter of 56 cm, 112 cm and 168 cm respectively.

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

π = 3.142

168 cm

Answer: 4927 cm²

Answer: 264 cm

SOLUTION 1 :

Step 1: Radius of big semi-circle → 168 ÷ 2

= 84 cm

Step 2: Radius of medium semi-circe → 112 ÷ 2

= 56 cm

Step 3: Radius of small semi-circle → 168 ÷ 2

= 28 cm

Step 4: Area of big semi circle → $\frac{1}{2}$ x π x 84 cm x 84 cm

= 11084.976 cm²

Step 5: Area of medium semi circle → $\frac{1}{2}$ x π x 56 cm x 56 cm

= 4926.656 cm²

Step 6: Area of small circle → $\frac{1}{2}$ x π x 28 cm x 28 cm

= 1231.664 cm²

Step 7: Area of the shaded part → 11084.976 cm² - 4926.656 cm² - 1231.664 cm²

= 4926.656 cm²

≈ 4927 cm²

Step 8: Circumference of big semi circle → $\frac{1}{2}$ x π x 168 cm

= 131.964 cm

Step 9: Circumference of medium semi circle → $\frac{1}{2}$ x π x 112 cm

= 87.976 cm

Step 10: Circumference of small semi circle → $\frac{1}{2}$ x π x 56 cm

= 43.988 cm

Step 11: Perimeter of shaded part → 131.964 cm + 87.976 cm + 43.988 cm

= 263.928 cm

≈ 264 cm