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 $10\mathrm{cm}×5\mathrm{cm}×4\mathrm{cm}$. 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.

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Solution

## 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 $=200-4×0.5495-27\phantom{\rule{0ex}{0ex}}=170.802c{m}^{3}\phantom{\rule{0ex}{0ex}}$

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