# In order to minimize neutron leakage from a reactor, the ratio of the surface area to the volume must be as small as possible. Assume that a sphere of radius a and a cube both have the same volume. Find the surface - to - volume ratio for (a) the sphere and (b) the cube. (c) Which of these reactor shapes would have the minimum leakage?

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In order to minimize neutron leakage from a reactor, the ratio of the surface area to the volume must be as small as possible. Assume that a sphere of radius a and a cube both have the same volume. Find the surface - to - volume ratio for (a) the sphere and (b) the cube. (c) Which of these reactor shapes would have the minimum leakage?

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Step 1

(a)

The ratio of the surface area (A) and the volume (V) of the sphere of the radius a can be calculated as,

Step 2

(b)

Consider the length of each side of the cube be l.

Since, the volume of the cube equal to that of the sphere, write the expression for the volume of the cube, and solve for the length of the side of the cube (l).

Step 3

The surface area of the cube ...

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