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The ratio of volume of a cube to that of a sphere, which will exactly fit inside the cube, is1). 6 : π2). 4 : π3). 5 : 3π4). 4 : 3 |
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Answer» We know that, Volume of CUBE = a3 where, a = side of the cube Volume of sphere = (4/3) π R3 where, r = radius of the sphere Let, Side of the cube = a Since, the sphere exactly fit INSIDE the cube ∴ Radius of the sphere = r = a/2 ∴ Required ratio $(= \;\frac{{{a^3}}}{{\frac{4}{3}{\RM{\;}} \times {\rm{\;\PI }} \times {{(\frac{a}{2})}^3}}} = \;\frac{{3 \times 8 \times \;{a^3}}}{{4 \times \;{\rm{\pi }} \times {\rm{\;}}{a^3}}} = \;\frac{6}{{\rm{\pi }}} = 6\;:{\rm{\pi }})$ |
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