Chapter 9 Measurement;: Length And Area Worksheet Page 28
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MEASUREMENT: LENGTH AND AREA (Chapter 9)
Investigation 3
A square peg in a round hole
In this investigation we explore the Opening Problem on page 170.
What to do:
1 Consider a square peg packed in a round container of
radius r cm.
a By dividing the square into two triangles, show
r cm
2
2
that the area of the square is 2r
cm
.
2
b Hence, show that the square occupies
of the
¼
container. Express this fraction as a percentage.
2 Now consider a round peg of radius r cm packed in
a square container.
2
2
a Show that the area of the square is 4r
cm
.
b Find the percentage of the container that is
r cm
occupied by the round peg.
3 Which design is more wasteful?
Review set 9
1 Which unit of area would be most appropriate for measuring:
a the area of a backyard
b the area of Western Australia
c the size of a postcard?
2 Convert:
a 12:9 cm to mm
b 3:95 km to m
c 2:43 m to cm
2
2
2
2
2
d 1459 cm
e 9:4 ha to m
f 12:8 cm
to m
to mm
3 Find the perimeter of:
a
b
c
1 54
.
m
10 m
2.62 m
8.2 cm
4 Find the area of:
8 cm
a
b
c
17 m
9 cm
8 m
2 3 . m
15 m
11 cm
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