Question

For each circle , work out​

Answer 1

Formulas

`\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}`

`\textsf{Area of a semicircle}=(1)/(2)\pi r^2 \quad \textsf{(where r is the radius)}`

`\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}`

`\textsf{Radius of a circle}=\sf (1)/(2)d\quad\textsf{(where d is the diameter)}`

`\textsf{Perimeter of a semicircle}=r(\pi +2) \quad \textsf{(where r is the radius)}`

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

`\implies \textsf{Area}=\sf \pi (2.7)^2=22.9\:\:cm^2\:(1\:d.p.)`

`\implies \textsf{Circumference}=\sf 2 \pi (2.7)=17.0\:\:cm\:(1\:d.p.)`

-----------------------------------------------------------------------

b) Diameter = 45 mm

`\sf \implies Radius =(45)/(2)=22.5\:\:mm`

`\implies \sf Area= \pi (22.5)^2=1590.4\:\:mm^2\:(1\:d.p.)`

`\implies \sf Circumference= 2 \pi (22.5)=141.4\:\:mm\:(1\:d.p.)`

Question 10

a) Radius = 8.5 cm

`\implies \sf Area=(1)/(2)\pi (8.5)^2=113.5\:\:cm\:(1\:d.p.)`

`\sf \implies Perimeter=8.5(\pi +2)=43.7\:\:cm\:(1\:d.p.)`

-----------------------------------------------------------------------

b) Radius = 24 mm

`\implies \sf Area=(1)/(2)\pi (24)^2=904.8\:\:mm\:(1\:d.p.)`

`\sf \implies Perimeter=24( \pi +2)=123.4\:\:cm\:(1\:d.p.)`

-----------------------------------------------------------------------

c) Diameter = 32 cm

`\sf \implies Radius =(32)/(2)=16\:\:cm`

`\implies \sf Area=(1)/(2)\pi (16)^2=402.1\:\:cm\:(1\:d.p.)`

`\sf \implies Perimeter=16( \pi +2)=82.3\:\:cm\:(1\:d.p.)`

-----------------------------------------------------------------------

d) Diameter = 15 m

`\sf \implies Radius =(15)/(2)=7.5\:\:m`

`\implies \sf Area=(1)/(2)\pi (7.5)^2=88.4\:\:m\:(1\:d.p.)`

`\sf \implies Perimeter=7.5( \pi +2)=38.6\:\:m\:(1\:d.p.)`