Chapter 12.5, Problem 42STP

To determine

To determine how tall is the tent’s center pole.

Answer to Problem 42STP

  $h=5.5\text{ feet}$

Explanation of Solution

Given:

Rectangular pyramid

Base diameter $=6\times 8$ feet

Tent holds $=$ volume of the tent $=88{\text{ feet}}^3$

Formula used:

Volume of the pyramid $=\frac{lwh}{3}\left[l=\text{length, }w\text{=}\text{width, }h\text{=}\text{height}\right]$

Calculation:

Rectangular pyramid has base diameter $=6\times 8$ feet.

Tent holds $=$ volume of the tent $=88{\text{ feet}}^3$

  $\Rightarrow$ Volume of the pyramid/tent $=\frac{lwh}{3}\left[l=\text{length, }w\text{= width, }h\text{= height}\right]$

  $\Rightarrow$ Volume of the pyramid/tent $=\frac{6\times 8\times h}{3}$

Volume of the tent $=88{\text{ feet}}^3$ given,

  $\Rightarrow$$88=\frac{48\times h}{3}$

  $\Rightarrow$ Height of the pyramid/tent $h=\frac{3\times 88}{48}$

  $\Rightarrow$ Height of the pyramid/tent $h=5.5\text{ feet}$

Conclusion:

Therefore, the tent’s center pole is $h=5.5\text{ feet}$ in height.