There are two spherical balls, each of radius 100 cm., lying on a perfectly horizontal floor and touching each other.
What is the diameter of the largest ball that can pass through the gap between the spheres and the floor ?

Since the distances between the radiuses of all three circles forms an isoceles triangle, with angle of CIRCLE-circle-CIRCLE of 90 degrees, we know that the other two angles are 45 degrees.Now knowing all three angles, and the hypotenuse (200 cm), we can use the "Sine Law" to define the space between the center of any of the big circles to the small circle which fits in between the two big circles. The Sine Law is (SinA/a)=(SinB/b). Where the center of the big circle is A, and the center of the little circle is B, their opposing sides are evidently a and b. Subbing values in, we know that Sin45/a=Sin90/200.
This comes out with an a-value of 141.4213562. To get the RADIUS of the little circle, we must subtract the RADIUS of the big circle, 100cm, which comes out to 41.42135624. Since, however, the question asks for the diameter of the little circle, we must double the radius, which gives a diameter of 82.84271247cm. Quite simple...I'm only 16 years old.

Posted by nathan on 2003-12-04 22:06:11