Chapter 5.2, Problem 74E

a.

To determine

To find the surface area of bat.

Answer to Problem 74E

The surface area of the bat is $230\sqrt[3]{16}\text{ square centimeters}$ .

Explanation of Solution

Given information:

The given statement is:

“The surface area $\text{S}$ (in square centimeters) of a mammal can be modelled by $\text{S}={\text{km}}^{2/3}$ , where $\text{m}$ is the mass (in grams) of the mammal and $\text{k}$ is a constant. The table shows the value of $\text{k}$ for different mammals.”

  

The mass of the bat is $32\text{ grams}$ .

Formula used:

The following formula is used:

  $\text{S}={\text{km}}^{2/3}$

Calculation :

The surface area of the bat is calculated by:

  $\begin{array}{l}\text{S}={\text{km}}^{2/3}\\ \text{S}=\left(57.5\right){\left(32\right)}^{2/3}\\ \text{S}=\left(57.5\right){\left(8\cdot 4\right)}^{2/3}\\ \text{S}=\left(57.5\right)2^2{\left(4\right)}^{2/3}\\ \text{S}=\left(57.5\right)2^2{\left(4\right)}^{2/3}\\ \text{S}=230{\left(4\right)}^{2/3}\\ \text{S}=230\sqrt[3]{16}\end{array}$

Hence, the surface area of the bat is $230\sqrt[3]{16}\text{ square centimeters}$ .

b.

To determine

To find the surface area of rabbit.

Answer to Problem 74E

The surface area of the rabbit is $975{\left(3.4\right)}^{2/3}\text{ square centimeters}$ .

Explanation of Solution

Given information:

The given statement is:

“The surface area $\text{S}$ (in square centimeters) of a mammal can be modelled by $\text{S}={\text{km}}^{2/3}$ , where $\text{m}$ is the mass (in grams) of the mammal and $\text{k}$ is a constant. The table shows the value of $\text{k}$ for different mammals.”

  

The mass of the rabbit is $3.4\text{ kilograms or 3}\text{.4}\times {\text{10}}^3\text{ grams}$ .

Formula used:

The following formula is used:

  $\text{S}={\text{km}}^{2/3}$

Calculation :

The surface area of the rabbit is calculated by:

  $\begin{array}{l}\text{S}={\text{km}}^{2/3}\\ \text{S}=\left(9.75\right){\left(3.4\times {10}^3\right)}^{2/3}\\ \text{S}=\left(9.75\right){10}^2{\left(3.4\right)}^{2/3}\\ \text{S}=\left(9.75\right)100{\left(3.4\right)}^{2/3}\\ \text{S}=\left(9.75\right)100{\left(3.4\right)}^{2/3}\\ \text{S}=975{\left(3.4\right)}^{2/3}\end{array}$

Hence, the surface area of the rabbit is $975{\left(3.4\right)}^{2/3}\text{ square centimeters}$ .

c.

To determine

To find the surface area of human.

Answer to Problem 74E

The surface area of the human is $1100{\left(59\right)}^{2/3}\text{ square centimeters}$ .

Explanation of Solution

Given information:

The given statement is:

“The surface area $\text{S}$ (in square centimeters) of a mammal can be modelled by $\text{S}={\text{km}}^{2/3}$ , where $\text{m}$ is the mass (in grams) of the mammal and $\text{k}$ is a constant. The table shows the value of $\text{k}$ for different mammals.”

  

The mass of the human is $\text{59 kilograms or 59}\times {\text{10}}^3\text{ grams}$ .

Formula used:

The following formula is used:

  $\text{S}={\text{km}}^{2/3}$

Calculation :

The surface area of the human is calculated by:

  $\begin{array}{l}\text{S}={\text{km}}^{2/3}\\ \text{S}=\left(11.0\right){\left(59\times {10}^3\right)}^{2/3}\\ \text{S}=\left(11.0\right){10}^2{\left(59\right)}^{2/3}\\ \text{S}=\left(11.0\right)100{\left(59\right)}^{2/3}\\ \text{S}=\left(11.0\right)100{\left(59\right)}^{2/3}\\ \text{S}=1100{\left(59\right)}^{2/3}\end{array}$

Hence, the surface area of the human is $1100{\left(59\right)}^{2/3}\text{ square centimeters}$ .