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A pen stand made of wood is in the shape...

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 xx 10 cm xx3.5 cm`.The radius of each of the depression is 0.5 cm and the depht is 1.4 cm .Find the volume of the wood in the entire stand correct to 2 decimal places.

Text Solution

Verified by Experts

The correct Answer is:
`523.53cm^3`
Radius of each conical depression `r=1/2 cm `
Depthe of each conical depression h=1.4 cm
Volume of the wood in the stand
= ( volume of the cuboid - volume of 4 conical depressions )
`=[(15 xx 10 xx 3.5 )-(4xx 1/3 pi r^2 h )] cm^2`
`=[525 -(4/3xx22/7xx 1/2xx1/2xx 1.4 )]cm^3`
`=(525 -(4.4)/(3))cm^3= ( 525 - 1.47 )cm^3`
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