Question

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins,respectively.The dimension of the cuboid are $10cm\times 5cm\times 4cm$.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 3cm.Find the volume of the wood in the entire stand.

Answer 1

Vol. of cuboid = $15\times 10\times 3.5=525c{m}^3$

vol. of wood taken out from four cavities = $4\times \frac{1}{3}\times \frac{22}{7}\times {0.5}^2\times 1.4=\frac{22}{15}=1.47c{m}^3$
vol. of wood in entire stand = 525-1.47
= 523.53 $c{m}^3$