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AREAS AND CIRCUMFERENCE OF CIRCLES

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
 

*************** END ***************


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

Mr. Yahya M (Badshah)

Category: Upper Primary | Added by: Admin (07/Apr/2017) | Author: Yahya Mohamed (Badshah) E W
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