A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are 15cm by 10cm by 3.5cm. The radius of each depression is 0.5 cm and the depth is 1.4cm. ____ is the amount of the wood in the entire stand.

Chapter/Topic: Direct and Inverse Proportions

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Detailed Solution

Since we know a pen stands in the shape of a cuboid with three conical depressions made in it to hold the pens.
We calculate the volume of the cuboidal pen stand by calculating the volume of the cuboid and subtract the volume of three conical depressions from it.
(i) Volume of cuboid:
Length of cuboid, l = 15cm
Breadth of cuboid, b = 10cm
Height of the cuboid, h = 3.5cm
Volume of cuboid = lbh
=15×10×3.5 = 525 cm3.
(ii) Volume of 3 conical depressions:
Height of the conical depression, h=1.4cm
Radius of base of conical depression,r=0.5cm
Volume of 3 conical depressions