Question

Part b)A foam protector is covered with PVC material to make it waterproof. Find the total surface area of a protector which is covered by PVCmaterial.

Answer 1

The diagram below would help

So from the diagram, we can see that

`\text{Volume of the foam = volume of cuboid - volume of cylinder }`

Volume of cuboid is given as

`\begin{gathered} V=l* w* h \\ \text{where }l=\text{length = 1.8 m} \\ w=\text{width = 300}mm=(300)/(1000)m=0.3m \\ h=\text{height }=\text{ 300}mm=(300)/(1000)m=0.3m \end{gathered}`

So volume of the cuboid becomes

`1.8*0.3*0.3=0.162m^3`

Volume of a cylinder is given as

`\begin{gathered} \pi r^2h \\ \text{where r = radius = }(diameter)/(2)=(150)/(2)mm=75mm=(75)/(1000)=0.075m \\ r=0.075m \\ h=1.8m \end{gathered}`

So, the volume of the cylinder becomes

`\begin{gathered} \pi r^2h \\ (22)/(7)*0.075^2*1.8 \\ =0.03182m^3 \end{gathered}`

Hence volume of the Foam becomes

`\begin{gathered} 0.162-0.03182 \\ 0.13018 \\ 0.13m^3 \end{gathered}`

Hence the answer is 0.13 cubic meter to 2 decimal places