A sphere and a cube of equal volumes both are made of iron and have similar surface. If both are cool in identical surrounding, at a lower temperature, then the ratio of the initial rates of loss of heat is

Options

A. `((pi)/(6))^(1//3):1`
B. `((3)/(4pi))^(-1//3):1`
C. `((3)/(4pi))^(2//3):1`
D. `1:1`

Answer

A

Explanation

Volume of sphere=Volume of cube
`(4pi)/(3)r^(3)=l^(3)`
`(r)/(l)=((3)/(4pi))^(1//3)` . . . (i)
`((dQ)/(dt))_(S)=4pir^(2)(T^(4)-T_(0)^(4))`
`((dQ)/(dt))_(C)=6l^(2)(T^(4)-T_(O)^(4))`
`((dQ//dt)_(S))/((dQ//dt)_(C))=(4pir^(2))/(6l^(2))`
Substitute r/l from equation (i), we have,
`=(4pi)/(6)xx((3)/(4pi))^(2//3)=((pi)/(6))^(1//3)`