1. The circumference of a circle is 123.2 cm.
Calculate :
(i) the radius of the circle in cm;
(ii) the area of the circle to the nearest cm2,
(iii) the effect on the area of the circle if the radius is doubled
Answers
A/Q
2
π
r
=
123.2
c
m
2πr=123.2cm
⇒
2
×
3.14
×
r
=
123.2
⇒
r
=
123.2
2
×
3.14
=
61.6
3.14
=
19.61
c
m
⇒2×3.14×r=123.2⇒r=123.22×3.14=61.63.14=19.61cm
(
i
i
)
(ii) area of circle
=
π
r
2
=
3.14
×
(
19.61
)
2
c
m
2
A
1
=
1207.49
c
m
2
=πr2=3.14×(19.61)2cm2A1=1207.49cm2
(
i
i
)
(ii) Radius of new circle
=
2
×
19.61
c
m
=
39.22
c
m
=2×19.61cm=39.22cm
A
2
,
a
r
e
a
=
3.144
×
(
39.22
)
2
c
m
2
=
4829.97
c
m
2
A
2
A
1
=
4829.97
c
m
2
1209.49
c
m
2
=
Step-by-step explanation:
1. Radius of Circle
Circumference = 123.2 cm
Radius => Circumference = 2 × \pi × r
Radius => 123.2 = 2 × 22/7 × r
=> r = 2 × 22 / 123.2 × 7
=> r = 2.5 cm
2. Area of the Circle
Radius of the Circle = 2.5 cm
Area of the Circle = \pi × r^2
= 22/7 × 2.5 × 2.5
= 19.642.... cm^2
3. If the Radius of the circle is doubled, then the Area of the Circle
Radius of the Circle = 2.5 cm
If the radius is doubled
2.5 × 2 = 5 cm
Area if the Circle = \pi × r^2
= 22/7 × 5 × 5
= 550/7
= 78.571.... cm^2