Chapter 8.5, Problem 35E

To determine

To check : Whether the given statement is true or false.

Answer to Problem 35E

The given statement is true

Explanation of Solution

Given information :

An aquarium contains water weighing $62.4lb/f{t}^3$ . The aquarium is in the shape of a cube where the length of each edge is 3ft. Each side of the aquarium is engineered to with stand 1000 pounds of force. This should be sufficient to withstand the force from water pressure.

Formula used :

  $\begin{array}{l}force={\displaystyle \underset{a}{\overset{b}{\int }}\left(edge\times weight\times h\right)}dh\\ \text{Where }h\text{ varies from }0\text{ to its edge}\text{.}\end{array}$

Calculation :

  $\begin{array}{l}\text{Force produce by water }={\displaystyle \underset{0}{\overset{3}{\int }}3\times 62.4\times sds}=3\times 62.4{\displaystyle \underset{0}{\overset{3}{\int }}sds}=\frac{3\times 62.4}{2}\times 3^2=842.4lb\\ \text{The force is less than 1000 pounds}\text{.}\end{array}$

Therefore,