year 8 maths

142 Chapter 3 Measurement and Pythagoras’ theorem
Example 12 Finding areas of semicircles and quadrants
Find the area of this quadrant and semicircle, correct to two decimal places.
a
b 5 km
3 m
SOLUTION
EXPLANATION
a
A = 1 4 × πr2
= 1 4 × π × 32
= 7.07 m 2 (to 2 d.p.)
The area of a quadrant is 1 the area of a circle with
4
the same radius.
b r = 5 2 = 2.5
A = 1 2 × πr2
= 1 2 × π × 2.52
The radius is half the diameter.
The area of a semicircle is 1 the area of a circle
2
with the same radius.
= 9.82 km 2 (to 2 d.p.)
Exercise 3E
UNDERSTANDING AND FLUENCY
1–6 3, 4–6(½)
4–6(½)
1 Evaluate without the use of a calculator.
22
a 3.14 × 10 b 3.14 × 4 c
7 × 7 d 22
7 × 72
2 Use a calculator to evaluate these to two decimal places.
a π × 5 2 b π × 13 2 c π × 3.1 2 d π × 9.8 2
3 What is the length of the radius in these shapes? Assume that all angles that look right angled
are 90°.
a
b
c
10 m
Example 10
7 km
2.3 mm
4 Use a calculator to find the area of these circles, correct to two decimal places.
a
b
c
3 cm
6 m
1.5 mm
d
10 km
e
3.4 cm
f
1.7 m
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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