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 perimeter of the first sector with radius 6 cm and angle 45°
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Answer
To find the length of the arc for the first sector, we use the formula:
ArcLength=360θ×2πr
Here, ( \theta = 45° ) and ( r = 6 ) cm.
So,
ArcLength=36045×2π×6=81×12π=1.5π≈4.71 cm
Step 2
Calculate the perimeter of the second sector with radius 3.5 cm and angle 45°
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Answer
Using the same formula for the second sector with radius 3.5 cm:
ArcLength=36045×2πr
Here, ( r = 3.5 ) cm:
ArcLength=36045×2π×3.5=81×7π=0.875π≈2.75 cm
Step 3
Add the straight edges of the sectors
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Answer
The straight edges of the sectors are the two radii, one of length 6 cm and one of length 3.5 cm:
TotalStraightEdges=6+3.5=9.5 cm
Step 4
Calculate the total perimeter of the shaded part
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Answer
Now, we sum the lengths of the arc and the straight edges:
