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Question

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 15cm by 10cm by 3.5cm. The radius of each of the depressions is 0.5cm and the depth is 1.4cm. Find the volume of wood in the entire stand (see Fig.).


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Solution

Given : Length of cuboid (l)=15cm

Breadth of cuboid (b)=10cm

Height of cuboid (h)=3.5cm

Radius of the conical part (r)=0.5cm

Height of the conical part (H)=1.4cm

TotalVolumewoodintheentirestand=VolumeofCuboidVolumeoffourconicalpart

=(l×b×h)4×(13πr2H)

=(15×10×3.5)4×13×227×0.52×1.4

=15×10×3510413×227×0.5×0.5×1.4

=15×354×13×227×12×12×1410

=52513×22×15

=5252215

=5251.466

=523.53cm3

Therefore, the volume of wood is523.53cm3


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