Five Marbles.
Five marbles of various sizes are placed in a conical funnel. Each marble is in contact with the adjacent marble(s). Also, each marble is in contact all around the funnel wall.
The smallest marble has a radius of 8mm. The largest marble has a radius of 18mm. What is the radius of the middle marble in (mm)?
The answer is 12.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let the distance of the smallest marble from the apex of the cone be x and the radii of the marbles be 8,a,b,c,18 respectively. The radii bear a constant ratio with the distances of the respective centres from the cone apex, say k. Then b=8((1+k)/(1-k))^2 and 18=8((1+k)/(1-k))^4 This gives b=12