The design below is made from two sectors of circles, centre O:
Calculate the perimeter of the shaded part - OCR - GCSE Maths - Question 8 - 2017 - Paper 1
Question 8
The design below is made from two sectors of circles, centre O:
Calculate the perimeter of the shaded part.
Give your answer correct to 3 significant figures.
Worked Solution & Example Answer:The design below is made from two sectors of circles, centre O:
Calculate the perimeter of the shaded part - OCR - GCSE Maths - Question 8 - 2017 - Paper 1
Step 1
Calculate the arc length of the first sector
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Answer
The first sector has a radius of 6 cm and an angle of 45 degrees. The formula for the arc length is:
L=360∘θ×2πr
For the first sector, substituting the values:
L1=36045×2π×6=81×12π=812π=1.5π≈4.71 cm
Step 2
Calculate the arc length of the second sector
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Answer
The second sector has a radius of 3.5 cm and an angle of 45 degrees. Applying the same formula:
L2=36045×2π×3.5=81×7π=87π≈2.75 cm
Step 3
Add the straight sides
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Answer
The two straight sides have a length of 6 cm (from the first sector) and 3.5 cm (from the second sector), so:
Total straight length=6+3.5=9.5 cm
Step 4
Calculate the total perimeter of the shaded part
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Answer
Now, add the arc lengths to the straight lengths:
Perimeter=L1+L2+Total straight length=4.71+2.75+9.5=16.96 cm
