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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.3 in Chapter 17 - Mensuration
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A cube of side 4 cm contains a sphere touching its sides.
Find the volume of the gap in between.
Answer:
Solution:
A cube's volume is the total amount of space it takes up in three dimensions. Six square faces make up a cube, a solid object in three dimensions with equal-length sides.
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)π 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. 
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