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Question 20
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 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions 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.


Solution

Given that,  length of cuboid pen stand (l) = 10 cm
Breadth of cuboid pen stand (b) = 5 cm
And height of cuboid pen stand (h) = 4 cm

Volume of cuboid =l×b×h=10×5×4 = 200 cm3
Also, radius of conical depression (r) = 0.5 cm
And height of (depth) of a  conical depression h1=2.1 cm
Volume of a conical depression = 13πr2h1

=13×227×0.5×0.5×2.1=22×5×51000=2240=1120=0.55 cm3
Also , given Edge of cubical depression (a)= 3cm
volume of cubical depression = (a)3=(a)3=27 cm3
So, volume of 4 conical depression
=4×1120=115 cm3
Hence the volume of wood in the entire pen stand

= Volume of cuboid pen stand – Volume of 4 conical
Depressions – Volume of  a cuboid depressions
=20011527=2001465=200  29.2 = 170.8 cm3
So, the required volume of the wood in the entire stand is 170.8 cm3.


Mathematics
NCERT Exemplar
Standard X

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