a circular path has to be constructed around a circular lunch is the outer and inner circumference of the pathway for 88 cm and 44 CM respectively find the width and area of the pathway
Answers
Answer:
The width is 7 cm.
The area of the path is 462 cm².
Step-by-step explanation:
Given : A circular path has to be constructed around a circular lawn.If the outer and inner circumferences of the path are 88cm and 44cm respectively.
To find : The width and area of the path ?
Solution :
Outer Circumference is C=2\pi RC=2πR
88=2\times \frac{22}{7} R88=2×
7
22
R
R=\frac{88\times 7}{2\times 22}R=
2×22
88×7
R=14R=14
Inner Circumference is c=2\pi rc=2πr
44=2\times \frac{22}{7} r44=2×
7
22
r
r=\frac{44\times 7}{2\times 22}r=
2×22
44×7
r=7r=7
The width is given by W=R-rW=R−r
W=14-7=7W=14−7=7
The width is 7 cm.
\text{Area of the path}=\pi (R^2- r^2)Area of the path=π(R
2
−r
2
)
\text{Area of the path}=\frac{22}{7}(14^2- 7^2)Area of the path=
7
22
(14
2
−7
2
)
\text{Area of the path}=\frac{22}{7}(196-49)Area of the path=
7
22
(196−49)
\text{Area of the path}=\frac{22}{7}(147)Area of the path=
7
22
(147)
\text{Area of the path}=462Area of the path=462
Therefore, the area of the path is 462 cm².
#Learn more
A circular path has to be constructed around a circular lawn. if the outer and inner circumferences of the path are 88 cm and 44 cm respectively, find the width and area of the path.
PLEASE MARK AS BRAINLIEST
outer circumference=88cm
inner circumference=44cm
circumference=2pir
pi=22/7
2×22/7×outer Radious=88
=>outer Radius = 14cm
2×22/7× inner Radius=44
=> inner Radius= 7cm
width of path = 14-7=7cm
width of path = 7cm
Area of path = outer Area - inner area
= pi14^2 - pi7^2
=pi×21×7
= 22×21
= 462cm^2