Find the diameter of circles having the
following areas.
5
1
(i) 5544 m2 (ii) 86-cm2 (iii) 346-cm?
8
2.
(iv) 616 m2 (v) 1386 m2
1620
Answers
Answer:
1) Diameter = 42 m
2) Diameter = 5.25 cm
3) Diameter = 46.93 cm
Step-by-step explanation:
To find : The diameter of circles having the following areas ?
Solution :
The diameter of the circle is d=2rd=2r
The area of the circle is A=\pi r^2A=πr
2
1) A_1=5544\ m^2A
1
=5544 m
2
5544=\frac{22}{7}\times (r_1)^25544=
7
22
×(r
1
)
2
(r_1)^2=\frac{5544\times 7}{22}(r
1
)
2
=
22
5544×7
r_1=\sqrt{1764}r
1
=
1764
r_1=42\ mr
1
=42 m
The diameter is d_1=2\times 42=84\ cmd
1
=2×42=84 cm
2) A_2=86\frac{5}{8}=\frac{693}{8}\ cm^2A
2
=86
8
5
=
8
693
cm
2
\frac{693}{8}=\frac{22}{7}\times (r_2)^2
8
693
=
7
22
×(r
2
)
2
(r_2)^2=\frac{693\times 7}{22\times 8}(r
2
)
2
=
22×8
693×7
r_2=\sqrt{27.5625}r
2
=
27.5625
r_2=5.25\ cmr
2
=5.25 cm
The diameter is d_2=2\times 5.25=10.5\ cmd
2
=2×5.25=10.5 cm
3) A_3=\frac{3461}{2}\ cm^2A
3
=
2
3461
cm
2
\frac{3461}{2}=\frac{22}{7}\times (r_3)^2
2
3461
=
7
22
×(r
3
)
2
(r_3)^2=\frac{3461\times 7}{22\times 2}(r
3
)
2
=
22×2
3461×7
r_3=\sqrt{550.6136}r
3
=
550.6136
r_3=23.46\ cmr
3
=23.46 cm
The diameter is d_3=2\times 23.46=46.93\ cmd
3
=2×23.46=46.93 cm