their centers' are 9cm apart, and their radius' are 6cm
2007-05-28 20:16:18 · 4 answers · asked by Idyllic 3 in Science & Mathematics ➔ Mathematics
If its only the overlapped area its 16.31922 cm²
Its almost impossible to explain it properly!
Draw the figure properly first.
The overlapping region is composed of two equal segment region.
You'll be able to draw a rhombus in that region which is necessary.
One of the diagonal is 3 cm
Find the other diagonal by using pythagoras theorem.
Calculate the angle subtende by using trigonometry.
Use cosine relation.
The angle comes out to be 1.4454 radians
Calculate the area of the sector. which comes to be
26.018 cm²
Then the area of the triangle inside. which comes to be 17.858 cm²
Subtract the two and you get area of one segment.
To get the total overlapped area double it = 16.31922 cm²
2007-05-28 20:19:56 · answer #1 · answered by Som™ 6 · 1⤊ 0⤋
Consider the common chord of the interesecting circles and the line connecting the two centers. This forms a triangular region comprising two right triangles of which both the length of one of the legs (4.5cm) and the length of the hypotenuse (6cm) are known. Using the Pythagorean theorem and the formula for the area of a triangle we can deduce that the triangular area is 17.85. The angle formed by the radius of the circle and the segment connecting the two centers can be found as the arccos(4.5/6) = 41.41 degrees. Doubling this and find the percentage of the circle this represents we get 23%. The area of the circle is 36pi = 113.09 and 23% of that is 26.02. So that means that half the overlapping area is 26.02-17.85 and the whole intersection is double that or approximately 16.37 cm^2
2007-05-28 20:31:45 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The intersection of the circles forms two segments of equal area. The area of a segment is
(r^2 / 2)(øs - sinøs)
where ø is the angle subtended by the segment.
Refer to the figure here: http://img292.imageshack.us/img292/4670/circlesnp0.png
The angle ø is given by arccos[(3r/2-d/2)/r] = arccos(4.5/6) = 0.723 radians.
The subtended angle øs = 2ø = 1.445 radians; sin(1.445)=0.992.
Therefore the area of one segment is 18*(1.445 - 0.992) = 8.154 cm^2. The overlapped area is two segments, so its area is
16.308 cm^2
2007-05-28 21:15:20 · answer #3 · answered by gp4rts 7 · 0⤊ 0⤋
shot in the dark here, 7.065
2007-05-28 20:22:52 · answer #4 · answered by gameboy200250213 1 · 0⤊ 0⤋