solid mensuration

posted by .

Find the area of a portion of a semicircle of radius 15 m that is outside the area of an inscribed square if the base of the square lies on the diameter of the semicircle.

Please include solution. Thanks.

  • solid mensuration -

    make a sketch, putting the complete figure on the x-y grid
    draw a line from the centre of the semicircle to the vertex of the square , calling that point P(x,y)

    so the base of the square is 2x and its height is y
    so clearly
    y = 2x

    also x^2 + y^2 = 15^2
    x^2 + (2x)^2 = 225
    5x^2 = 225
    x^2 = 45
    x = 3√5
    y = 6√5
    area of square = 2xy
    = 2(3√5)(6√5) = 180

    area of semicircle = (1/2)π(15)^2 = 225π/2

    area between square and semicircle
    = 225π/2 - 180 or appr 173.43

    check my arithmetic

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    A rectangle is constructed with its base on the diameter of a semicircle with radius 5 cm and with two vertices on the semicircle. What are the dimensions of the rectangle with maximum area?
  2. Calculus

    A rectangle is constructed with its base on the diameter of a semicircle with radius 5 cm and with two vertices on the semicircle. What are the dimensions of the rectangle with maximum area?
  3. calculas

    find the perimeter of the rectangle with maximum area that can be inscribed in a semicircle of radius 2 ft. if two of its vertices are on the diameter of the semicircle and the other two are on the semicircle.
  4. Calculus

    Find the rectangle of largest area that can be inscribed in a semicircle of radius R, assuming that one side of the rectangle lies on the diameter of the semicircle. NOTE: Let L denote the length of the side that lies on the diameter …
  5. Geometry - semicircle inside isosceles triangle

    Isosceles triangle ABC has sides of length AB=AC=25 and BC=40 . Find the area of a semicircle inscribed in triangle ABC with diameter along BC . Please help I do not know how to start....
  6. pre-calc

    a semicircle of radius r=3x is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle 1. express the area A if the rectangke as a function 2 express the perimeter P of the rectamgle as a function …
  7. Solid Mensuration

    The area of a regular hexagon inscribed in a circle is equal to 166.28 square cm. If the circle is inscribed in a square, find the difference between the area of the square and the hexagon.
  8. Calculus

    Find the area of the largest rectangle that fits inside a semicircle of radius 10 (one side of the rectangle is along the diameter of the semicircle).
  9. precalc

    A Norman window has the shape of a square with a semicircle mounted on it. Find the width of the window if the total area of the square and the semicircle is to be 240 ft squared
  10. math

    if the area of the square inscribed in a semicircle is 2cm^2,find the area of the square inscribed in a full circle

More Similar Questions