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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.

 

    • Posted by Rosy Maheshwari 8 years, 9 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Naveen Sharma 8 years, 9 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

    1Thank You

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