A sphere and a cube of same material and same total surface area are placed in the same evacuated space turn by turn after they are heated to the same temperature. Find the ratio of their initial rates of cooling in the enclosure.

Options

A. 1
B. `sqrt(pi)`
C. `sqrt((pi)/(6))`
D. `(1)/(sqrt(6))`

Explanation

For sphere
`sigmaT^(4)S=m_(1)C.((-d theta)/(dt))_("sphere")`
for cube
`sigmaT^(4).S=m_(2)C((-d theta)/(dt))_("cube")`
`therefore(((-d theta)/(dt))_("sphere"))/((-(d theta)/(dt))_("cube"))=(m_(2))/(m_(1))=(V_(2))/(V_(1))[S=6a^(2)=(4pir^(2))]=sqrt((pi)/(6))`