Question

The difference between the area of the outer and the
inner square of a circle is 63 cm^2 and O is the centre
of the circle. Find the area of the circle.
77 cm^2
80 cm^2
99 cm^2
50 cm^2​

Answer 1

Answer:

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Answer 2

Answer:

Area of the circle will be 99 cm² (Option C).

Step-by-step explanation:

In the figure attached, there are two squares formed inside and outside the circle with center O and radius r.

First we will calculate the area of the inner square.

Since diagonals of a square intersect each other at the center

Therefore, side of the inner square will be = $\sqrt{r^{2}+r^{2}}$

                                                                       = $r\sqrt{2}$

Area of the square inscribed in the circle = Side²

                                                                    = $(r\sqrt{2})^{2}$

                                                                    = 2r²

Now area of the square outside the circle = (2r)²

                                                                      = 4r²

Since difference between the area of outer and inner squares = 63 cm²

Therefore, 4r² - 2r² = 63

2r² = 63

r = $\sqrt{\frac{63}{2}}$

Area of the circle = $\pi r^{2}$

                             = $\pi (\sqrt{\frac{63}{2}})^{2}$

                             = $\frac{22}{7}\times \frac{63}{2}$

                             = 99 cm²

Therefore, option C. is the correct option.

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