A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.
Solution:
Given, side of cube = 4 cm
A cube contains a sphere touching its sides
We have to find the volume of the gap in between
Volume of gap in between = volume of cube - volume of sphere
Volume of cube = (side)³
= (4)³
= 64 cm³
Since the sphere is inside the cube, the diameter of the sphere = 4 cm
So, radius of the sphere = 2 cm
Volume of sphere = 4/3 πr³
Where, r is the radius of the sphere
= 4/3 (22/7)(2)³
= 4(22)(8)/21
= 32(22)/21
= 704/21
= 33.52 cm³
Volume of gap in between = 64 - 33.52
= 30.48 cm³
Therefore, the volume of the gap in between is 30.48 cm³.
✦Try This: A cube of side 5 cm contains a sphere touching its sides. Find the volume of the gap in between.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13
NCERT Exemplar Class 9 Maths Exercise 13.4 Problem 6
A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.
Summary:
A cube of side 4 cm contains a sphere touching its sides. The volume of the gap in between is 30.48 cm³
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