Question

In the game of pool, the fifteen balls are packed tightly into a triangular rack. The diameter of all the balls are the same. If the height of the rack is BC = 33 cm. Find the diameter of a ball.

Answer 1

Hello there.

In the game of pool, the fifteen balls are packed tightly into a triangular rack. The diameter of all the balls are the same. If the height of the rack is BC = 33 cm. Find the diameter of a ball.

6.648 cm.

Answer 2

(264(3^1/2)-198)/39 = approximately 6.648 cm.
Let x be the diameter of the ball. Stacking the balls will create a kite. From there it can be derived that the height of the kite is x(3^1/2).
There will be 2 kites in the stack, and 2 half balls + increment between the ball and tip of triangle which is x/2.
Adding these altogether = 33, we get x as stated above.