Question

pool eight - ball pool is a popular game played on a pool table that has six pockets. in eight - ball pool, there are 7 striped balls, 7 solid - colored balls, and a black eight ball. at the beginning of each game, players position the 15 balls in a rack in preparation for the first shot.
9.96 in.
11.5 in.
a. find the area contained by the rack using an appropriate two - dimensional model. round your answer to the nearest tenth of a square inch.
$\text{in}^2$
b. approximate the area covered by a single ball to the nearest tenth of a square inch.
$\text{in}^2$

Explanation:

Step1: Calculate area of the triangular rack

The rack is triangular. The area formula for a triangle is $A=\frac{1}{2}bh$, where $b = 11.5$ inches and $h=9.96$ inches. So $A=\frac{1}{2}\times11.5\times9.96$.
$A=\frac{1}{2}\times11.5\times9.96 = 5.75\times9.96=57.27\approx57.3$ square - inches.

Step2: Estimate area of a single ball

There are 15 balls in the rack. Assume the balls fill the rack area relatively uniformly. Divide the area of the rack by the number of balls. Let $A_{ball}$ be the area of a single ball. Then $A_{ball}=\frac{57.3}{15}$.
$A_{ball}=\frac{57.3}{15}=3.82\approx3.8$ square - inches.

Answer:

a. $57.3$
b. $3.8$