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ioda
1 year ago
9

S To minimize neutron leakage from a reactor, the ratio of the surface area to the volume should be a minimum. For a given volum

e V , calculate this ratio for (a) a sphere
Physics
1 answer:
erastovalidia [21]1 year ago
3 0

To minimize neutron leakage from a reactor, the ratio of the surface area to the volume should be a minimum. For a given volume V the ratio of the sphere will be \frac{4.83598}{c^{\frac{1}{3} } }.

We know that the surface area and volume of the sphere is given by:

A=4 \pi r^{2}\\V=\frac{4}{3} \pi r^{3}

Therefore, the ratio between the surface area and the volume for the sphere will be:

\frac{A}{V}=\frac{4 \pi r^{2}\\}{\frac{4}{3} \pi r^{3}}=\frac{3}{r}

Equating the volume to the constant c, we will find the value of r.

V=c=\frac{4}{3} \pi r^{3}\\r= (\frac{3c}{4\pi} )^{\frac{1}{3} }

Substituting the value of r in the ration between surface area and volume, we get:

\frac{A}{V}=\frac{3}{ (\frac{3c}{4\pi} )^{\frac{1}{3} }}

Calculating the constants, we get:

\frac{4.83598}{c^{\frac{1}{3} } }

Hence, the ration between surface area and volume is \frac{4.83598}{c^{\frac{1}{3} } }

To learn more about surface area and volume of sphere, refer to:

brainly.com/question/4387241

#SPJ4

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