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The shape below is formed from two semicircles and a straight line - OCR - GCSE Maths - Question 13 - 2018 - Paper 6

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The shape below is formed from two semicircles and a straight line. The radius of the large semicircle is 8 cm. The radius of the small semicircle is 1 cm. Find an... show full transcript

Worked Solution & Example Answer:The shape below is formed from two semicircles and a straight line - OCR - GCSE Maths - Question 13 - 2018 - Paper 6

Step 1

Find the circumference of the large semicircle

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Answer

The circumference of a full circle is given by the formula: C=2πrC = 2\pi r. Since we only need half for the semicircle, the circumference of the large semicircle (radius = 8 cm) is:

Circumferencelarge=12×2π×8=8π cm\text{Circumference}_{\text{large}} = \frac{1}{2} \times 2\pi \times 8 = 8\pi \text{ cm}

Step 2

Find the circumference of the small semicircle

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Answer

Similarly, for the small semicircle (radius = 1 cm):

Circumferencesmall=12×2π×1=π cm\text{Circumference}_{\text{small}} = \frac{1}{2} \times 2\pi \times 1 = \pi \text{ cm}

Step 3

Combine parts to find the exact perimeter

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Answer

The exact perimeter of the shaded shape is the sum of the circumferences of the two semicircles, plus the straight line segment (length = t):

P=Circumferencelarge+Circumferencesmall+t=8π+π+t=9π+t cmP = \text{Circumference}_{\text{large}} + \text{Circumference}_{\text{small}} + t = 8\pi + \pi + t = 9\pi + t \text{ cm}

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