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The surface area of a sphere and cube ar...

The surface area of a sphere and cube are equal.Find the ratio of their volumes.[take `pi=22/7`]

Text Solution

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Surface Area of a cube `= 6a^2`
Surface Area of a sphere ` = 4pir^2`
We are given,
`4pir^2 = 6a^2`
`=>r/a = sqrt(3/(2pi))`
Now, ratio of their volume,
Volume of sphere`/`Volume of cube = `(4/3pir^3)/(a^3)`
`=4/3pi(r/a)^3 = 4/3pi(3/(2pi))**sqrt(3/(2pi))`
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