Question

Silvia wants to construct a cylindrical water tank made out of polyethylene. Calculate the volume of the empty water tank. Then proceed to find the mass of the object based on the standard density of the material and the volume of the object.Given:Height=8ftWidth=5ftDensity= 0.900 g/cm3

Answer 1

Given:

height of the cylinder = 8ft

width of the cylinder - 5ft

density = 0.900 g/cm3

The volume V of a cylinder can be calculated using the formula:

`\begin{gathered} V\text{ = }\pi r^2h \\ Where\text{ r is the radius } \\ and\text{ h is the height} \end{gathered}`

The radius is half the width.

Substituting the given values:

`\begin{gathered} V\text{ = }\pi*((5)/(2))^2*8 \\ =\text{ 157.08 ft}^3 \end{gathered}`

The mass m, volume v and density are related by the formula:

`density\text{ = }\frac{mass}{volume\text{ }}`

Substituting and solving for the mass:

`\begin{gathered} 0.900\text{ }(g)/(cm^3)\text{ = }\frac{mass}{157.08\text{ ft}^3} \\ mass\text{ = 0.900 }(g)/(cm^3)\text{ }*\text{ 157.08 }\frac{28316.8\text{ cm}^3}{ft^3} \\ =\text{ 4003202.65 g} \\ =\text{ 4003.2 kg} \end{gathered}`

Answer Summary

`\begin{gathered} Volume\text{ = 157.08 ft}^3 \\ mass\text{ = 4003.2 kg} \end{gathered}`