If the circumference of a circle is equal to sum of the circumference of two circles of radius 10 cm and 24 cm, Calculate the radius of the larger circle (in cm). *
Answers
Given-
The diameter of the two circles are
d1=36 cm⇒ radius r1=2d1=236 cm=18 cm and
d2=20 cm⇒ radius r2=2d2=220 cm=10 cm.
∴ The circumference C1=2πr1=2π×18cm=36π cm and
The circumference C2=2πr2=2π×10 cm=20π cm
So C1+C2=(36+20)π cm=56π cm.
This is the circumference C of the resulting circle.
∴C=C1+C2=56π cm
Let the radius of this circle be r.
Now, the radius of a circle =2πcircumference
∴r=2π56π cm=28 cm.
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Hope's it helpful to you
Answer:
Radius of the first circle r
1
=
2
10
=5 cm
Radius of the second circle r
2
=
2
24
=12 cm
∴ Sum of their area = πr
1
2
+πr
2
2
⇒π5
2
+π12
2
⇒25π+144π=169π
Let the radius of the larger circle be r
∴Area=πr
2
According to the question -
⇒πr
2
=169π
⇒r
2
=169
⇒r=
169
=13 cm
∴Radius of the new circle=13 cm
Then diameter of the larger circle=13×2=26 cm