Answer:
If the temperature of the solar surface is 5800 K then the approximate temperature of the sunspot is a) 4400 K.
Step-by-step explanation:
The most straightforward way to solve this is using Stefan-Boltzmann law that states that I the energy radiated per unit surface area per unit time (watt per unit area
) of a black body is proportional to the fourth power of the temperature T of the body:

with
being the Stefan constant.
A black body is an idealized physical body that is a perfect absorber because it absorbs all incident electromagnetic radiation and is also an ideal emitter. The Sun is considered to be a black body at different layers and different temperatures.
We are told that the intensity of a sunspot
is found to be 3 times smaller than the intensity emitted by the solar surface
, that means that:

then using the expression of Stefan-Boltzmann law we get that

we cross out
and use the fourth root in each side of the equation
![\sqrt[4]{T_(sunspot) ^(4)}=\frac{\sqrt[4]{T_(surface) ^(4)}}{\sqrt[4]{3}}](https://img.qammunity.org/2020/formulas/physics/high-school/szuk5b7oiqhs9obt5i9mx9sdr9vnt3p5qz.png)
![T_(sunspot)=\frac{T_(surface)}{\sqrt[4]{3} }](https://img.qammunity.org/2020/formulas/physics/high-school/6qw2b2450tha7ro8frmufdc0zat9n2lou1.png)
then we use that


So finally we get that
