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A Cube of side 4cm contains …

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A Cube of side 4cm contains a sphere touching its sides.Find the voloume of the gap in between.

 

  • 1 answers

Naveen Sharma 7 years, 2 months ago

Ans. Side of Cube (a) = 4 cm

Volume of Cube = \(a^3 = 4 \times 4 \times 4 = 64 cm^3\)

As the Sphere touch the side of Cube

So, Diameter of Sphere = 4 cm

Radius of Sphere(r) = 4/2 = 2 cm

Volume of Sphere = \({4\over 3} \times \pi \times r^3 = {4\over 3} \times {22\over 7}\ \times 8 = {704\over 21} = 33.5 cm^3\)

Volume of Gap = Volume of Cube - Volume of Sphere 

=> 64 - 33.5 = 30.5cm3

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