The diagram shows a semicircle with diameter 16 cm. 16 cm © EAGLE BEACON GLOBAL Work out the area of the semicircle. Give your answer correct to 3 significa...
Question 1 Report
The diagram shows a semicircle with diameter 16 cm.
Work out the area of the semicircle. Give your answer correct to 3 significant figures. (3)
Answer Details
This question finds the area of a semicircle from its diameter, using the formula for the area of a full circle halved.
The radius is half the diameter: \[ \text{Radius} = \frac{16}{2} = 8 \text{ cm} \] [1 mark]
The area of a semicircle is half of \(\pi r^2\): \[ \text{Area} = \frac{1}{2} \times \pi \times 8^2 = 32\pi \] [1 mark]
Evaluating and rounding to 3 significant figures: \[ 32\pi = 100.5\ldots \approx 101 \text{ cm}^2 \] [1 mark]
A common mistake is to use the diameter, rather than the radius, inside \(\pi r^2\); halving the diameter first is essential before squaring, since the area formula is defined in terms of the radius.
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