AREAS AND CIRCUMFERENCE OF CIRCLES

Before we start, let’s Note on the use of PI (π)

We understand that PI can be expressed as 3.14 or ²²/₇

We shall use PI ²²/₇ if we find that the radius or Diameter is easily Divisible by 7 such as 7, 14, 21, 28, 42, 2.1, 3.5, 1.4 and the like. Any other dimension which is not divisible by 7 such as 3, 4, 12, 10 and the like, we use PI 3.14.

Examples:

1.    What is the area of a circle with radius of 7 m ?

Radius = r = 7

Area = π × r²

          = π × 7²

          = π × 7 × 7 but π = ²²/₇

          = ²²/₇ × 7 × 7

          = 154 m²

2.    What is the area of a circle with Diameter of 28 cm?

Remember that Diameter is twice a radius. So in order to get a radius from diameter, divide it by 2.

Radius = Diameter ÷ 2

Radius = 28 ÷ 2

Radius = r = 14 cm

Area = π × r²

          = π × 14²

          = π × 14 × 14 but π = ²²/₇

          = ²²/₇ × 14 × 14

          = 616 cm²

3. Find the area of semi-circle with radius 10cm

Area = ¹/₂ π × r²

            = ½ x 3.14 x 10 x 10

            = ½ x 314

            = 154cm²

4. What is the area and circumference of the figure below?

Area = ¾ x π × r²

                        = ¾ x ²²/₇ x 28 x 28

            = 1848 m²

Circumference = ³/₄ πD + D

Note: Diameter (D) = 2r, in the question we know that 28m is the radius, so in order to get diameter we multiply radius by 2. That is 2 x 28m = 56m then:

¾ x ²²/₇ x 56 + 56 = 132m + 56m = 188m

Therefore Circumference = 188m

5. Find the area and circumference of the below sector:

Area = ^θ/₃₆₀  x  πr²

θ = 18°, π = 3.14, r = 4cm

Area = ^18°/_360° x 3.14 x 4 x 4

            = ¹/₂₀ x 50.24

            = 2.512 cm²

Circumference = ^θ/₃₆₀ x πD + D

θ = 18°,  π = 3.14,  D = r x 2 = 8cm

Circumference = ^18°/_360° x 3.14 x 8 + 8

                        = ¹/₂₀ x 25.12 + 8

                        = 1.256 + 8

                        = 9.256cm

6. Find the area and circumference of the below figure:

Area = ^θ/₃₆₀  x  πr²

θ = 140°, π = ²²/₇, r = 21 cm

Area = ^140°/_360° x ²²/₇ x 21 x 21

            = 539 cm²

Circumference = ^θ/₃₆₀ x πD + D

θ = 140°,  π = ²²/₇,  D = r x 2 = 42cm

Circumference = ^140°/_360° x ²²/₇ x 42 + 42

                        = 51 ¹/₃  +  42

                        = 93 ¹/₃ cm
 

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In case of any question or comment be free to write down:
A lot of Thanks

Mr. Yahya M (Badshah)