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.

Question

Frankfurter

Mathematics

7 September, 20:26

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.

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Answers (2)

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Mac · Answer 1

(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.

Andrew Dean · Answer 2

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.