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Home » Area between the circumferences of two concentric circles is . The inner circle has a circumference of cm, Find the radius of the outer circle.
Area between the circumferences of two concentric circles is 2464c{{m}^{2}}. The inner circle has a circumference of 132 cm, Find the radius of the outer circle.
Class 10 | Frank | ICSE | Maths | Mensuration I
Area between the circumferences of two concentric circles is 2464c{{m}^{2}}. The inner circle has a circumference of 132 cm, Find the radius of the outer circle.

Given that,

Area between the circumferences of two concentric circles is 2464c{{m}^{2}}

Circumference of inner circle =132 cm

Circumference =2\pi r

132=2\pi r

r=132/2\pi

r=\left( 132\times 7 \right)/\left( 2\times 22 \right)

Radius of circle (r) =21 cm

Radius of the inner circle is 21 cm.

Area of inner circle =\pi {{r}^{2}}

=22/7\times {{21}^{2}}

Area of inner circle 1386c{{m}^{2}}

Area of outer circle = area of inner circle + area of concentric circles

=\left( 1386+2464 \right)c{{m}^{2}}

Area of outer circle =3850c{{m}^{2}}

Let assume  R be the radius of outer circle,

Area of outer circle =\pi {{R}^{2}}

3850=\pi {{R}^{2}}

{{R}^{2}}=\left( 3850\times 7 \right)/22

{{R}^{2}}=1225

R=\sqrt{1225}

R =35 cm

Hence, the radius of the outer circle is 35 cm.

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