This is the Important question of class 10 Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD.
Here the edge cube is given , a cone of maximum size is carved out then find the volume of the remaining material.
This is the Question Number 03, Exercise 17.4 of M.L Aggarwal.
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From a cube of edge 14 cm, a cone of maximum size is carved out. Find the volume of the remaining material.
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Given edge of the cube, a = 14 cm
Radius of the cone, r = 14/2 = 7 cm
Height of the cone, h = 14 cm
Volume of the cube = a3
= 143
= 14×14×14
= 2744 cm3
Volume of the cone = (1/3)r2h
= (1/3)×(22/7)×72×14
= 22×7×14/3
= 2156/3 cm3
Volume of the remaining material = Volume of the cube- Volume of the cone
= 2744-2156/3
= (3×2744-2156)/3
= (8232 – 2156)/3
= 6076/3
Hence the volume of the remaining material is
.