Question

a concrete drain is 10 m long with an outside diameter of 1 m and an inside diameter of 0.8 m determine the volume of concrete required to make the drain to the nearest tenth of cubic metre

Answer 1

Let x be the volume of the cylinder with diameter 1m

Let y be the volume of the cylinder with diameter 0.8m

The volume of concrete required to make the drain is:

$V=x-y$

___________

Volume of a cylinder:

$V=\pi\cdot(\frac{d}{2})^2\cdot h$

h is the height

d is the diameter

For the given drain:

$\begin{gathered} V=(\pi\cdot(\frac{d_x}{2})^2\cdot h)-(\pi\cdot(\frac{d_y}{2})\cdot h)_{} \\ \\ V=((\frac{d_x}{2})^2-(\frac{d_y}{2})^2)\pi\cdot h \\ \\ V=(\frac{(d_x)^2}{4}-\frac{(d_y)^2}{4})\pi\cdot h \\ \\ V=(\frac{(d_x)^2-(d_y)^2}{4})\pi\cdot h \\ \\ \end{gathered}$$\begin{gathered} V=(\frac{(1m)^2-(0.8m)^2}{4})\pi\cdot10m \\ \\ V=\frac{1m^2-0.64m^2}{4}\cdot\pi\cdot10m \\ \\ V=\frac{0.36m^2}{4}\cdot\pi\cdot10m \\ \\ V=\frac{3.6\pi}{4}m^3 \\ \\ V=0.9\pi m^3 \\ \\ V\approx2.8m^3 \end{gathered}$

Then, the volume of concrete required is 2.8 cubic meter