1.

Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

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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