the area of a circle is doubled when its radius R is increased by a therefore radius r equals
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Step-by-step explanation:
The area of a circle is doubled when its radius r is increased by a.
Area of original circle=πr
2
New radius = (r+a)
Area of new circle = π(r+a)
2
Given,
2πr
2
=π(r+a)
2
=>2r
2
=r
2
+a
2
+2ra
=>r
2
=a
2
+2ra
=>r
2
−2ra−a
2
=0
=>r=
2(1)
−(−2a)±
(−2a)
2
−4(1)(−a)
2
=>r=
2
2a±
4a
2
+4a
2
=>r=
2
2a±
8a
2
=>r=a±
2
a
Now,
r=a−
2
a is not possible as r cannot be negative.
∴r=a+
2
a
=a(1+
2
)
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