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Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube. |
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Answer» Let side of cube is `a` and radius of sphere is `r`. As sphere exactly fit inside the cube, `:. a = 2r` Ratio of volume of cube to that of sphere,`V_c/V_s = a^3/(4/3pir^3)` `V_c/V_s = (2r)^3/(4/3pir^3)` `=>V_c/V_s = (8r^3)/(4/3pir^3) = 6/pi` So, the required ratio is `6:pi`. |
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