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

SOLUTION

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

$\begin{gathered} V=l\times w\times h \\ \text{where }l=\text{length = 1.8 m} \\ w=\text{width = 300}mm=\frac{300}{1000}m=0.3m \\ h=\text{height }=\text{ 300}mm=\frac{300}{1000}m=0.3m \end{gathered}$

So volume of the cuboid becomes

$1.8\times0.3\times0.3=0.162m^3$

Volume of a cylinder is given as

$\begin{gathered} \pi r^2h \\ \text{where r = radius = }\frac{diameter}{2}=\frac{150}{2}mm=75mm=\frac{75}{1000}=0.075m \\ r=0.075m \\ h=1.8m \end{gathered}$

So, the volume of the cylinder becomes

$\begin{gathered} \pi r^2h \\ \frac{22}{7}\times0.075^2\times1.8 \\ =0.03182m^3 \end{gathered}$

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