Chapter 0.9, Problem 19E

(a)

To determine

The volume of a full cord of firewood.

Answer to Problem 19E

  $V=128{\text{ ft}}^3$

Explanation of Solution

Given:

Measurement or full cord

  $\begin{array}{l}8\times 4\times 4\text{ ft}\\ \text{or,}\\ 8\times 8\times 2\text{ ft}\end{array}$

Calculation:

The volume of full cord if the measurement is $8\times 4\times 4=128{\text{ ft}}^3$ .

And

The volume of full cord if the measurement is $8\times 8\times 2=128{\text{ ft}}^3$ .

Conclusion:

Hence, the volume of full cord of firewood is $128{\text{ ft}}^3$ .

(b)

To determine

The volume of a short cord of firewood.

Answer to Problem 19E

  $V=48{\text{ ft}}^3$

Explanation of Solution

Given:

The length of short cord $=2\frac{1}{2}\text{ ft}=\frac{2\times 1+1}{2}\text{ ft}=\frac{3}{2}\text{ ft}$

Calculation:

The volume of short cord,

  $\begin{array}{l}V=8\times 4\times \frac{3}{2}\\ V=48{\text{ ft}}^3\end{array}$ .

Conclusion:

Hence, the volume of short cord of firewood is $48{\text{ ft}}^3$ .

(c)

To determine

The height of the store.

Answer to Problem 19E

  $h=10.67\text{ ft}$

Explanation of Solution

Given:

Volume of full cord $V=128{\text{ ft}}^3$

Length $l=12\text{ ft}$

Width $w=2\text{ ft}$

Formula used:

Volume = length × width × height

Calculation:

Volume of the full cord,

  $\begin{array}{l}V=l\times w\times h\\ 128=12\times 2\times h\\ h=\frac{128}{24}\\ h=10.67\text{ ft}\end{array}$ .

Conclusion:

Hence, the height of the store is equal to the 10.67 ft.