An Important Question of M.L Aggarwal book of class 10 Based on Mensuration Chapter for ICSE BOARD.
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 is given. If the radius of each of the depression and the depth is also given.
Then find the volume of the wood in the entire stand.
This is the Question Number 06, Exercise 17.4 of M.L Aggarwal.
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 depression is 0.5 cm and the depth is 1.4 cm. Find the volume of the wood in the entire stand, correct to 2 decimal places.
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Dimensions of the cuboid = 15 cm× 10 cm × 3.5 cm
Volume of the cuboid = 15×10×3.5 = 525 cm3
Radius of each depression, r = 0.5 cm
Depth, h = 1.4 cm
Volume of conical depression = (1/3)r2h
= (1/3)×(22/7)×0.52×1.4
= 22×0.25×1.4/21
= 7.7/21 cm3
Volume of 4 such conical depressions = 4×7.7/21
= 1.467 cm3
Volume of wood in the stand = Volume of the cuboid- Volume of 4 conical depressions
= 525-1.467
= 523.533
= 523.53 cm3
Hence the volume of the wood in the stand is 523.53 cm3.