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Maths

Circles

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Semi-circles and quarter circles

The perimeter of a semi-circle can be found by using the equation π x r², which is commonly used to calculate the area of a whole circle:

  • area of a semi-circle: 1/2 x π x r2
  • area of a quarter circle: 1/4 x π x r2
  • perimeter of a semi-circle: π x r + 2 x r
  • perimeter of a quarter circle: 1/2 x π x r + 2 x r

Example

A window in the shape of a semi-circle has a radius of 40 cm. Work out:

  1. The area
  2. The length of the sealant strip needed for the perimeter

Solution

    • Area = 1/2 x π x r2

    • 1/2 x π x 402

    • Area = 2513 cm2

    •  
    • Perimeter = π x r + 2 x r

    • π x 40 + 2 x 40

    • 125.7 + 80

    • Perimeter = 205.7 cm

    •  

Question

Jenny has a patio in her garden. Its shape is a quarter circle with a radius of 3m.

  1. How much space is there on the patio?
  2. What is its perimeter?

toggle answer

Answer
    • We need to find the area.

    • Area = 1/4 x π x r2

    • 1/4 x π x 32

    • Area = 7.07m2

    •  
    • Perimeter = 1/2 x π x r + 2 x r

    • 1/2 x π x 3 + 2 x 3

    • 4.7 + 6

    • Perimeter = 10.7m

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