Question

A sphere and cube of same material and same volume are heated up to the same temperature and
allowed to cool in the same surroundings. The ratio of the amounts of radiations emitted will be
​

Answer 1

The ratio of the amounts of radiations emitted will be (π/6)^1/3 : 1

Explanation:

Solution:

Q = σAt(T^4−To^4)

If T,T0,σ and t are same for both bodies then

Q(sphere) / Q(cube) = A(sphere) / A(cube) =4πr^3 / 6a^2  .......(i)

But according to problem, volume of sphere = volume of cube

=> 4/3πr^3=a^3

=> a=(4/3π)^1/3 r

substituting the value of a in Equation. (i) we get

Q(sphere) / Q(cube) = 4πr^2 / 6a^2

=4πr^2 / 6{(4/3π)^1/3 r}^2 = 4πr^2 / 6{(4/3π)^2/3 r^2)

= (π/6)^1/3 : 1

thus the ratio of the amounts of radiations emitted will be (π/6)^1/3 : 1

Also learn about ratio and proportion

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