Calculus question?

A square is inscribed in the circle x^2+y^2=32. Find the area of the square.

7 Answers

Relevance
  • 1 month ago
    Favorite Answer

    x² + y² = 32

    (x - 0)² + (y - 0)² = (√32)²

    The typical equation of a circle is: (x - xo)² + (y - yo)² = R² → where:

    xo: abscissa of center → 0 in your case

    yo: ordinate of center → 0 in your case

    R: radius of circle → √32 in your case → then the diameter is: d = 2√32

    As the square is inscribed in the circle, the diameter of the circle is the diagonal of the square.

    The surface area of the square is:

    a = s² ← where s is one of the sides of the square

    According the Pythagorean's theorem, you can see that:

    s² + s² = d² ← where d is the diagonal of the square, i.e. the diameter of the circle

    2s² = d²

    s² = d²/2 → recall: a = s²

    a = d²/2 → recall: d = 2√32

    a = (2√32)²/2

    a = (4 * 32)/2

    a = 64

  • David
    Lv 7
    1 month ago

    Circle equation: x^2 + y^2 = 32

    Circle center: (0, 0)

    Radius of circle: square root of 32 = 4 times square root of 2

    Diameter of circle: 8 times square root of 2

    Sides of square using Pythagoras: 8

    Area of inscribed square: 8 times 8 = 64 square units

  • 1 month ago

    The area of a square is the half the square of the diagonal.

    The area of a square is the half the square of the diameter of the circumscribed circle.

    The area of a square is the double the square of the radius of the circumscribed circle.

    The square of the radius of the circle is 32, so the area of a square is 64 square units.

  • 1 month ago

    Since the square is inscribed in the circle,

    the diagonal distance between opposite corners is √32.

    x^2 + y^2 = √(32)^2, where 'c' is the diagonal (which is √32) across the square,

    and forms the hypotenuse of a right triangle.

    Since this is a square, we know that x = y.

    So we know that x^2 + x^2 = (16)^2.

  • How do you think about the answers? You can sign in to vote the answer.
  • 1 month ago

    Let the apex of the square on the circle be (x, y) in the first quadrant. But x=y for a square.

    Area, A = 4yx=4x^2.

    x^2+y^2=32.

    x^2 + (x)^2 = 32.

    4x^2 =64

    A = 64.

    Or, you may use the diagonal length = diameter of the circle = 2√32 =8√2.

    Area = 8√2*8√2/2 = 64.

  • TomV
    Lv 7
    1 month ago

    The diagonal of the square is the diameter of the circle = 2√32 = 8√2

    The square of the diagonal is twice the square of the side of the square:(8√2)² = 2s²

    s² = 2(8)²

    s² = 64

    Area of the square is the square of the side of the square:

    A = s² = 64

    Ans: 64

  • Anonymous
    1 month ago

    Calculus answer

Still have questions? Get your answers by asking now.