Answer:
Formulas
[tex]\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Area of a semicircle}=\dfrac{1}{2}\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]
[tex]\textsf{Radius of a circle}=\sf \dfrac{1}{2}d\quad\textsf{(where d is the diameter)}[/tex]
[tex]\textsf{Perimeter of a semicircle}=r(\pi +2) \quad \textsf{(where r is the radius)}[/tex]
Use the above formulas to calculate the various measurements, remembering to calculate the radius first when given the diameter.
Question 9
a) Radius = 2.7 cm
[tex]\implies \textsf{Area}=\sf \pi (2.7)^2=22.9\:\:cm^2\:(1\:d.p.)[/tex]
[tex]\implies \textsf{Circumference}=\sf 2 \pi (2.7)=17.0\:\:cm\:(1\:d.p.)[/tex]
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b) Diameter = 45 mm
[tex]\sf \implies Radius =\dfrac{45}{2}=22.5\:\:mm[/tex]
[tex]\implies \sf Area= \pi (22.5)^2=1590.4\:\:mm^2\:(1\:d.p.)[/tex]
[tex]\implies \sf Circumference= 2 \pi (22.5)=141.4\:\:mm\:(1\:d.p.)[/tex]
Question 10
a) Radius = 8.5 cm
[tex]\implies \sf Area=\dfrac{1}{2}\pi (8.5)^2=113.5\:\:cm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=8.5(\pi +2)=43.7\:\:cm\:(1\:d.p.)[/tex]
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b) Radius = 24 mm
[tex]\implies \sf Area=\dfrac{1}{2}\pi (24)^2=904.8\:\:mm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=24( \pi +2)=123.4\:\:cm\:(1\:d.p.)[/tex]
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c) Diameter = 32 cm
[tex]\sf \implies Radius =\dfrac{32}{2}=16\:\:cm[/tex]
[tex]\implies \sf Area=\dfrac{1}{2}\pi (16)^2=402.1\:\:cm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=16( \pi +2)=82.3\:\:cm\:(1\:d.p.)[/tex]
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d) Diameter = 15 m
[tex]\sf \implies Radius =\dfrac{15}{2}=7.5\:\:m[/tex]
[tex]\implies \sf Area=\dfrac{1}{2}\pi (7.5)^2=88.4\:\:m\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=7.5( \pi +2)=38.6\:\:m\:(1\:d.p.)[/tex]
