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

Explanation:

Step1: Recall area formula for triangle

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

Step2: Identify base and height values

From the image, the base $b = 9.96$ inches and the height $h=11.5$ inches.

Step3: Calculate the area

Substitute the values into the formula: $A=\frac{1}{2}\times9.96\times11.5$. First, $9.96\times11.5 = 114.54$. Then, $\frac{1}{2}\times114.54=57.27$. Rounding to the nearest tenth, $A\approx57.3$ square - inches.

Step4: Assume ball is a circle

A pool - ball is approximately a circle. The standard diameter of a pool - ball is 2.25 inches, so the radius $r=\frac{2.25}{2}=1.125$ inches.

Step5: Calculate area of a single ball

The area formula for a circle is $A = \pi r^{2}$. Substitute $r = 1.125$ into the formula: $A=\pi\times(1.125)^{2}=\pi\times1.265625$. Using $\pi\approx3.14$, we get $A\approx3.14\times1.265625 = 3.9740625\approx4.0$ square - inches.

Answer:

a. $57.3$ in²
b. $4.0$ in²