# A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens.

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A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Figure)

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Radius of conical depression, r = 0.5 cm.

(Depth) height, h = 1.4 cm.

Volume of 1 depression which is conical,

Volume of such 4 depressions

= 4 x $\frac{11}{30}cm^3$

$\frac{44}{30}$cm3

∴ Total volume of wooden pen-stand,

= (15 x 10 x 3.5) -  $\frac{44}{30}$

= 525 – 1.47

= 523.53 cm3