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A square is inscribed in circle of radiu...

A square is inscribed in circle of radius R, a circle is inscribed in the square, a new square in the circle and so on for n times.
Sum of the areas of all circles is

A

`4piR^(2)(1-(1/2)^(n))`

B

`2piR^(2)(1-(1/2)^(n))`

C

`3piR^(2)(1-(1/3)^(n))`

D

`piR^(2)(1-(1/2)^(n))`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • If a square is inscribed in a circle of radius 7 cm, then find the area of the square (in cm^(2) ).

    A
    49
    B
    98
    C
    196
    D
    392

  • A square is inscribed in a circle then another circle is inscribed in the square . Another square is then inscribed in the circle. Finally a circle is inscirbed in the innermost square . Thus there are 3 circles and 2 squares as shown in the figure . The radius of the outer - most circle is R . What is the ratio of sum of circumference of all the circles to the sum of perimeters of all the squares ?

    A
    `(2 + sqrt(3))pi R `
    B
    `(3 + sqrt(2)) pi R `
    C
    `3 sqrt(3) pi R `
    D
    none of these

  • A square is inscribed in a circle then another circle is inscribed in the square . Another square is then inscribed in the circle. Finally a circle is inscirbed in the innermost square . Thus there are 3 circles and 2 squares as shown in the figure . The radius of the outer - most circle is R . What is the sum of areas of all the squares shown in the figure ?

    A
    `3R^(2) `
    B
    `3sqrt(2)R^(2) `
    C
    `(3)/(sqrt(2)) R^(2) `
    D
    none of these