Chapter 11.3, Problem 6P

To determine

To calculate:

The width of the pyramid

Answer to Problem 6P

The width of the pyramid at the height of $86m$ is $95.77m$ .

Explanation of Solution

Given information:

The width of pyramid decreases by $1.57m$ for successive $1m$ of height.

Common difference: $d=1.57m$

The width at the height of $1m$ : $229.22m$

Formula used:

  $a_n=a_1+\left(n-1\right)d$

Calculation:

The change in height from $1m$ to $86m$ :

  $86-1=85m$

The width of pyramid decreases by $1.57m$ for each additional $1m$ of height.

The width has decreased by

  $85m\times 1.57m=133.45meters$

The width at the height of $1m$ : $229.22m$

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ a_{86}=229.22-133.45\\ a_{86}=95.77m\end{array}$

The width of the pyramid at the height of $86m$ is $95.77m$ .