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A circle has radius 5 cm - OCR - GCSE Maths - Question 4 - 2019 - Paper 1

Question 4

A circle has radius 5 cm. (a) Work out the circumference of the circle. (b) Work out the area of the circle.

Worked Solution & Example Answer:A circle has radius 5 cm - OCR - GCSE Maths - Question 4 - 2019 - Paper 1

Step 1

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Answer

To find the circumference of a circle, we use the formula:

$C = 2 \pi r$

where $r$ is the radius. Here, the radius $r = 5$ cm. Substituting the value into the formula:

$C = 2 \pi \times 5 = 10\pi$

Using an approximate value of $\pi \approx 3.14$ , we calculate:

$C \approx 10 \times 3.14 = 31.4 \text{ cm}$

Thus, the circumference of the circle is approximately 31.4 cm.

Step 2

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Answer

To find the area of a circle, we use the formula:

$A = \pi r^2$

where $r$ is the radius. Given that the radius $r = 5$ cm, we substitute:

$A = \pi \times (5)^2 = 25\pi$

Using the same approximation for $\pi$ as before ( $\pi \approx 3.14$ ):

$A \approx 25 \times 3.14 = 785 \text{ cm}^2$

Therefore, the area of the circle is approximately 78.5 cm².

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