Question

the difference between the area of the outer and the inner square of a circle is 63 cm2 and 0 is the centre of the circle find the area of the circle​

Answer 1

Answer:

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Answer 2

The area of the circle is 99 ${cm}^{2}$.

Step-by-step explanation:

Given:

• The difference between the area of the outer and the inner square of a circle is 63 cm2.
• 0 is the centre of the circle .

Let the side of outer square is a cm.

Let the side of inner square is b cm and r cm is the radius of circle.

The figure is shown in the attachment.

$\rightarrow \: {a}^{2} - {b}^{2} = 63 \\ \rightarrow \:a = 2r \\ \rightarrow \: \cos(45) = \frac{r}{b} \\ \: \: \: \: \: \: b = r \sqrt{2}$

Putting value of a and b in difference of area of square

$\rightarrow \: {(2r)}^{2} - {(r \sqrt{2}) }^{2} = 63 \\ \rightarrow \:4 {r}^{2} - 2 {r}^{2} = 63 \\ \rightarrow \:2 {r}^{2} = 63 \\ \rightarrow \:\pi {r}^{2} = \pi \times \frac{63}{2} \\ \rightarrow \:area = \frac{22}{7} \times \frac{63}{2} \\ \rightarrow \:area = 99 \: {cm}^{2}$

The area of the circle is 99 $</strong><strong> </strong><strong>{cm}^{2}</strong><strong> </strong><strong>$