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.
37.3 in²
b. approximate the area covered by a single ball to the nearest tenth of a square inch.
11.5 in²

Explanation:

Step1: Identify shape and formula

The rack is triangular. The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Substitute values

Given $b = 11.5$ inches and $h=9.96$ inches. So $A=\frac{1}{2}\times11.5\times9.96$.

Step3: Calculate

$A = 5.75\times9.96=57.27\approx57.3$ square - inches.

For the area of a single ball, assume the balls are circular. First, we need to find the diameter of a ball. In a standard 15 - ball rack, if we assume the balls are tightly packed in the triangular rack. The base of the triangle is formed by 5 balls. So the diameter $d$ of a single ball is approximately $\frac{11.5}{5}=2.3$ inches. The radius $r=\frac{d}{2}=1.15$ inches.
The area formula for a circle is $A=\pi r^{2}$.
Substitute $r = 1.15$ inches into the formula: $A=\pi\times(1.15)^{2}\approx3.14\times1.3225 = 4.15265\approx4.2$ square - inches.

Answer:

a. $57.3$
b. $4.2$