Sphere to cube

Geometry Level 3

A sphere has volume $x \text{ m}^3$ and surface area $x \text{ m}^2$ . Keeping its diameter as body diagonal, a cube is made which has volume $a \text{ m}^3$ and surface area $b \text{ m}^2$ . What is the ratio $a:b?$

3^{\frac 12}

\frac13

3^{-\frac 12}

1 solution

Nanda Kumar
May 18, 2015

Here (4/3) (pi)r^3 = 4(pi)r^2; so r =3m So body diagonal of cube = 6m Edge length of cube = 2(3)^1/2 So surface are = 72m^2 Volume = 24(3)^2 Ratio of volume to surface are = 1/[(3)^1/2]

Sphere to cube

1 solution

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