Chapter 11.8, Problem 14WE

To determine

To Estimate: The area of one star.

Answer to Problem 14WE

  $0.006m^2$

Explanation of Solution

Given: A carnival game has a white dart board $5m$ long and $2m$ wide on which $100$ red stars are painted. Each player tries to hit a star with the dart. Before trying it you notice that only $3$ shots out of the previous $50$ hit a star.

Ratio of area of stars to the area of boards.

  $\frac{3}{50}or\frac{6}{100}$

Area of dartboard.

  $\begin{array}{l}A=lb\\ A=5(2)=10m^2\end{array}$

Area of hundred stars

  $\begin{array}{l}10\times \frac{3}{50}\\ =\frac{3}{5}{m}^2\end{array}$

Area of single star

  $\begin{array}{l}A=\frac{ar(allstars)}{100}\\ A=\frac{\frac{3}{5}}{100}=\frac{3}{500}=0.006m^2\end{array}$

Hence, area is $0.006m^2$ .