Answer:
Three balls are placed inside a cone such that each ball is in contact with the edge of the cone and the next ball.
If the radii of the balls are 20 cm, 12 cm, and r cm from top to bottom, what is the value of r?
Step-by-step explanation:
Three balls are placed inside a cone such that each ball is in contact with the edge of the cone and the next ball.
If the radii of the balls are 20 cm, 12 cm, and r cm respectively, what is the value of r?
Solution
Consider the following diagram.
Using similar triangles, (12 + r)/(12 minus r) = 32/8 = 4.
therefore 12 + r = 48 minus 4r
therefore 5r = 36 implies r = 7.2 cm.
What if the radii of the three balls were 20 cm, r cm, and 10 cm?
If the top sphere has radius, x, and the bottom sphere has radius, y, find r in terms of x and y.