Question

A pen stand made of wood is in the shape of a cuboid with four conical depression and a cubical depression to hold the pens and pins , respectively . The dimension of the cuboid are $10\mathrm{cm}\times 5\mathrm{cm}\times 4\mathrm{cm}$. The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm . The edge of the cubical depression is 3 cm . Find the volume of the wood in the entire stand.

Answer 1

The dimensions of the cuboid = 10 cm × 5 cm × 4 cm
Volume of the total cuboid = 10 cm × 5 cm × 4 cm = 200 cm³
Radius of the conical depressions, r = 0.5 cm
Depth, h = 2.1 cm
Volume of the conical depression = $\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\mathrm{\pi }{\left(0.5\right)}^2\left(2.1\right)=0.5495$ cm³
Edge of cubical depression, a = 3 cm
Volume of the cubical depression = $a^3=3^3=27c{m}^3$
Volume of wood used to make the entire stand = Volume of the total cuboid − volume of conical depression − volume of cubical depression
$$\begin{gathered} =200-4\times 0.5495-27 \\ =170.802c{m}^3 \end{gathered}$$