Question

For each circle , work out​

Answer 1

Answer:

Formulas

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

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

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

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

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

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

$\sf \implies Radius =\dfrac{45}{2}=22.5\:\:mm$

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

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

Question 10

a)  Radius = 8.5 cm

$\implies \sf Area=\dfrac{1}{2}\pi (8.5)^2=113.5\:\:cm\:(1\:d.p.)$

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

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

b)  Radius = 24 mm

$\implies \sf Area=\dfrac{1}{2}\pi (24)^2=904.8\:\:mm\:(1\:d.p.)$

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

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

c)  Diameter = 32 cm

$\sf \implies Radius =\dfrac{32}{2}=16\:\:cm$

$\implies \sf Area=\dfrac{1}{2}\pi (16)^2=402.1\:\:cm\:(1\:d.p.)$

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

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

d)  Diameter = 15 m

$\sf \implies Radius =\dfrac{15}{2}=7.5\:\:m$

$\implies \sf Area=\dfrac{1}{2}\pi (7.5)^2=88.4\:\:m\:(1\:d.p.)$

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