Posted by Cathy on Saturday, December 1, 2012 at 7:07am.
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 - Reiny, Saturday, December 1, 2012 at 9:38am
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
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
Answer This Question
More Related Questions
- Solid Mensuration - The area of a regular hexagon inscribed in a circle is equal...
- Calculus - Find the rectangle of largest area that can be inscribed in a ...
- Geometery - How do I solve this? On my assignment it says find the area inside ...
- Calculus - Show that the rectangle with the largest area that is inscribed ...
- calculas - find the perimeter of the rectangle with maximum area that can be ...
- math - 1. A wire of length x is bent into the shape of a square. Express the ...
- geometry - I need to find the area of the shaded portion of a circle with a ...
- Math 117 - 1.) A rectangular solid and a circular cylinder have the same volume ...
- calculus - 1. A solid is constructed so that it has a circular base of radius r ...
- math (solid mensuration) - A light is placed 5 ft. from the center of a globe 3 ...