Mathematics

Question

please respond asap!!!
please respond asap!!!

2 Answer

  • Hello!

    The answer is:

    The difference between the circle and the square is:

    [tex]Difference=4\pi -8[/tex]

    Why?

    To solve the problem, we need to find the area of the circle and the area of the square, and then, subtract them.

    For the square we have:

    [tex]side=2\sqrt{2}[/tex]

    We can calculate the diagonal of a square using the following formula:

    [tex]diagonal=side*\sqrt{2}[/tex]

    So,

    [tex]diagonal=2\sqrt{2}*\sqrt{2}=2*(\sqrt{2})^{2}=2*2=4units[/tex]

    The area will be:

    [tex]Area_{square}=side^{2}= (2\sqrt{2})^{2} =4*2=8units^{2}[/tex]

    For the circle we have:

    [tex]radius=\frac{4units}{2}=2units[/tex]

    The area will be:

    [tex]Area_{Circle}=\pi *radius^{2}=\pi *2^{2}=\pi *4=4\pi units^{2}[/tex]

    [tex]Area_{Circle}=4\pi units^{2}[/tex]

    Then, the difference will be:

    [tex]Difference=Area_{Circle}-Area{Square}=4\pi -8[/tex]

    Have a nice day!

  • ANSWER

    [tex]4\pi - 8[/tex]

    EXPLANATION

    The diagonal of the square can be found

    using Pythagoras Theorem.

    [tex] {d}^{2} = {(2 \sqrt{2} )}^{2} + {(2 \sqrt{2} )}^{2} [/tex]

    [tex]{d}^{2} = 4 \times 2+ 4 \times 2[/tex]

    [tex]{d}^{2} = 8+ 8[/tex]

    [tex]{d}^{2} = 16[/tex]

    Take positive square root

    [tex]d = \sqrt{16} = 4[/tex]

    The radius is half the diagonal because the diagonal formed the diameter of the circle.

    Hence r=2 units.

    Area of circle is

    [tex]\pi {r}^{2} =\pi \times {2}^{2} = 4\pi[/tex]

    The area of the square is

    [tex] {l}^{2} = {(2 \sqrt{2)} }^{2} = 4 \times 2 = 8[/tex]

    The difference in area is

    [tex]4\pi - 8[/tex]

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