Light from an ideal spherical blackbody 15.0 cm in diameteris analyzed by using a diffraction grating that has 3850 lines/cm.When you shine this light through the grating, you observe that thepeak-intensity wavelength forms a first-order bright fringe at +-14.4from the central bright fringe. (a) What is the temperature of the blackbody?(b) How long will it take this sphere to radiate 12.0 MJ of energyat constant temperature?

Please explain with steps.

Explain the blackbody radiation and its effect?

You have stated that the convective area is πr^2. Please explain this. πr^2 is the area for a circle, not a sphere. It should be 4πr^2 as this is equal to the surface area of the sphere as you have done correctly in the radiative area.  A conv= 4πr^2*3*293-292 = 0.377 A rad = 4πr^2*0.2*5.67x10^-8*(292^4-291^4) = 0.144 I have tried to multiply the convective area by 4πr^2 instead of πr^2 but it is giving me an incorrect total heat transfer rate of 0.377+0.144 = 0.521 the correct answer is supposed to be 0.236