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Q.


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 then, the volume of wood in the entire stand (see Fig) is


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a

525c m 3  

b

523.53c m 3  

c

526.47c m 3  

d

528c m 3    

answer is B.

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Detailed Solution

It is given,
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.
The depth is 1.4 cm.
Question ImageVolume of the wood present in the stand = Volume of cuboid – 4(Volume of conical depression) …...eq (1)
Volume of cone, v= 1 3 π r 2 h  
Given, r = 0.5 cm, h = 1.4 cm
Therefore, Volume of conical depression                           
⇒v= 1 3 π r 2 h. ⇒v= 1 3 × 22 7 ×0.5×0.5×1.4 ⇒v= 1 3 ×22×0.5×0.5×0.2 ⇒v=0.367c m 3   Using formula for Volume of cuboid =l×b×h  
Given, dimensions of cuboid =15cm×10cm×3.5cm  
Therefore, Volume of cuboid, v=l×b×h  
⇒v=15×10×3.5 ⇒v=525c m 3   Substituting these values in eq (1), we get
Volume of wood present in the stand is
⇒Volume of cuboid – 4 (Volume of conical depression)
⇒525−4 0.367 ⇒525−1.468 ⇒523.53c m 3   The pen stand has wood of volume 523.53c m 3   present in it.
Hence, option (2) is correct.
 
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