This question is Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here the side of cube is given which contains a sphere touching its sides.
Find the volume of the gap in between.
This is the Question Number 11, Exercise 17.3 of M.L Aggarwal.
Deepak BoraNewbie
A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.
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Given side of the cube, a = 4 cm
Volume of the cube = a3
= 43
= 4×4×4
= 64 cm3
Diameter of the sphere = 4 cm
So radius of the sphere, r = d/2 = 4/2 = 2 cm
Volume of the sphere = (4/3)r3
= (4/3)×(22/7)×23
= 33.523
= 33.52 cm3 (approx)
Volume of the gap in between = 64 – 33.52
= 30.48
= 30.5 cm3 (approx)
Hence the volume of the gap between the cube and sphere is 30.5 cm3.