Question

a training field is formed by a rectangle and two semicircles. the rectangle is 96 m long and 63 m wide. what is the length of a training track running around the field? use the value 3.14 for pie, do not round the answer.

Answer 1

Given the geometry of the training field as shown below:

The length of the training track is evaluated by summing the lengths of the rectangle ABED and the length (circumference) of the semi-circles AFE and ACD.

$\text{Length of track = AB + BCD + DE + AFE}$

where

$AB\text{ = DE = 96 m}$

The circumferences of the semi-circles AFE and ACD are similar and are evaluated as

$\begin{gathered} \text{circumference = 2}\times\pi\times r \\ \text{where} \\ r\text{ = }\frac{d}{2}=\frac{63}{2} \\ \pi=3.14 \end{gathered}$

thus,

$\begin{gathered} \text{circumference = 2}\times3.14\times\frac{63}{2}\text{ = 197.82 m} \\ \text{thus, the circumference of the semicircles is 197.82 m } \end{gathered}$

The total length of the training field is thus evaluated as

$\begin{gathered} 96\text{ + 197.82 + 96 + 197.82} \\ =\text{ }587.64\text{ m} \end{gathered}$

Hence, the length of the training track running around the field is 587.64 m.