I get 1.44 as my answer but that is wrong. how do i solve this one?

First off you need to determine the amount of energy that a lightbulb emits in an hour.

100 W = 100 J/s

Therefore in one hour the lightbulb uses 60 x 60 x 100 = 360000 J

Now we need to calculate the power of the radiation of the blackbody

Power = A x sigma x T^4

calculate total surface area

6 x 0.012^2 = 0.000864 m^2

convert Temp from Celsius to Kelvin

90 = 363 K

Sigma = stefan boltzmann's constant = 5.67 x 10^-8

Plug it all into original equation for blackbody including energy from lightbulb

Remember Power = Energy/time

360000 = 0.000864 x (5.67 x 10^-8) x (363)^4 x time

360000 / (0.000864 x 5.67 x 10^-8 x 363^4) = time

time = 423232.6847 seconds

time in days = Answer / (24 x 60 x 60)

time in days = 4.90 (3 s.f.) days

Same method as in the link.

Note area A = 6 x 0.012² m²

Energy produced by 100W bulb in 1 hour = 100 x 60 x 60 J

If you don't get the right answer, post your detailed working for checking.