Respuesta :
We are asked to determine the weight of a bed of water with dimensions 1.83m x 1.93m x 0.248m. To do that we will determine the mass using the following formula:
[tex]m=\rho V[/tex]Where:
[tex]\begin{gathered} m=\text{ mass} \\ \rho=\text{ density} \\ V=\text{ volume} \end{gathered}[/tex]To determine the volume we will use the fact that the bed has the shape of a rectangular prism and therefore its volume is the product of its dimensions, like this:
[tex]V=\lparen1.83m)\left(1.93m\right)\left(0.248m\right)[/tex]Solving the operations we get:
[tex]V=0.88m^3[/tex]The density of water is given by:
[tex]\rho=1000\text{ kg/m}^3[/tex]Substituting in the formula for the mass:
[tex]m=\lparen1000\text{ kg/m}^3)\left(0.88m^3\right)[/tex]Solving the operations:
[tex]m=880kg[/tex]Now, to determine the weight we use the following formula:
[tex]W=mg[/tex]Where:
[tex]\begin{gathered} W=\text{ weight} \\ m=\text{ mass} \\ g=\text{ acceleration of gravity} \end{gathered}[/tex]Substituting the values:
[tex]W=\left(880kg\right)\left(9.8\text{ m/s}^2\right?[/tex]Solving the operation:
[tex]W=8624N[/tex]Since the weight is 8624 N this means that the weight will not be tolerated.
