Chapter 1, Problem 57SGR

To determine

To calculate: The body mass index of different cats provided their circumference of Rib Cage and Leg Length.

  $\begin{array}{ccc}\text{Cat}& \begin{array}{r}\text{Circumference of}\\ \text{Rib Cage (in}\text{.)}\end{array}& \begin{array}{c}\text{Leg Length}\\ \text{(in)}\end{array}\\ \text{Missy}& 17.5& 4.0\\ \text{Oscar}& 15.0& 3.5\\ \text{Whiskers}& 20.3& 3.8\end{array}$

Answer to Problem 57SGR

The body mass index of Missy cat is $\text{18}\text{.70}$ , Oscar cat is $\text{15}\text{.88}$ and Whiskers cat is $\text{23}\text{.44}$ .

Explanation of Solution

Given information:

The circumference of Rib Cage and Leg Length of cats is provided below,

  $\begin{array}{ccc}\text{Cat}& \begin{array}{r}\text{Circumference of}\\ \text{Rib Cage (in}\text{.)}\end{array}& \begin{array}{c}\text{Leg Length}\\ \text{(in)}\end{array}\\ \text{Missy}& 17.5& 4.0\\ \text{Oscar}& 15.0& 3.5\\ \text{Whiskers}& 20.3& 3.8\end{array}$

Formula used:

The body mass index that is BMI of cat provided its circumference around its rib cage and the length of its back leg from knee to ankle is,

  $\text{BMI}=\frac{\frac{\text{circumference}}{0.7062}-\text{leg length}}{0.9156}-\text{leg length}$

Calculation:

Consider the circumference of Rib Cage and Leg Length of cats that is provided below,

  $\begin{array}{ccc}\text{Cat}& \begin{array}{r}\text{Circumference of}\\ \text{Rib Cage (in}\text{.)}\end{array}& \begin{array}{c}\text{Leg Length}\\ \text{(in)}\end{array}\\ \text{Missy}& 17.5& 4.0\\ \text{Oscar}& 15.0& 3.5\\ \text{Whiskers}& 20.3& 3.8\end{array}$

Recall that the body mass index that is BMI of cat provided its circumference around its rib cage and the length of its back leg from knee to ankle is,

  $\text{BMI}=\frac{\frac{\text{circumference}}{0.7062}-\text{leg length}}{0.9156}-\text{leg length}$

For the Missy cat, body mass index is, replace circumference by $17.5$ and keg length by $4.0$ ,

  $\begin{array}{c}\text{BMI}=\frac{\frac{17.5}{0.7062}-4.0}{0.9156}-\text{4}\text{.0}\\ \approx \text{18}\text{.70}\end{array}$

For the Oscar cat, body mass index is, replace circumference by $15.0$ and keg length by $3.5$ ,

  $\begin{array}{c}\text{BMI}=\frac{\frac{15.0}{0.7062}-3.5}{0.9156}-\text{3}\text{.5}\\ \approx \text{15}\text{.88}\end{array}$

For the Missy cat, body mass index is, replace circumference by $20.3$ and keg length by $3.8$ ,

  $\begin{array}{c}\text{BMI}=\frac{\frac{20.3}{0.7062}-3.8}{0.9156}-\text{3}\text{.8}\\ \approx \text{23}\text{.44}\end{array}$

Thus, the body mass index of Missy cat is $\text{18}\text{.70}$ , Oscar cat is $\text{15}\text{.88}$ and Whiskers cat is $\text{23}\text{.44}$ .