Chapter 1.4, Problem 47AYU

To determine

To find: The area of the square

Answer to Problem 47AYU

The area of the square is $18$ square units

Explanation of Solution

Given:

  

Calculation:

Compare the equation of circle $x^2+y^2=9$ with standard equation $x^2+y^2=r$ . On comparing the given equation with the standard form, we get $r^2=9$ or $r$ as $3$

Therefore the radius of the circle is $3$ units

The diameter of the circle is $2\times 3=6$ units

From the given figure the red line represents both the diameter of the circle and the diagonal of the square

Therefore the diagonal of square must be equal to diameter of the circle

This implies diagonal of the square $=6$

Assume the side of square is x units

Therefore the diagonal of square is $\sqrt{2x}$ units

This implies as follows

  $\sqrt{2x}=6$

  $x=\frac{6}{\sqrt{2}}$

The area of square is calculated as follows

  $Area=x^2$

  $={\left(\frac{6}{\sqrt{2}}\right)}^2$

  $=\frac{36}{2}$

  $=18$

Conclusion:

Hence,the required area of the square is $18$ square units