Math help please

I am starting radiation therapy school in January and after I signed up I was notified I have to take an on-line math course. The problem is how to do the math isn’t explained very well. I’m starting on a new section now, and I’m totally lost. Can anyone explain how the answers to these questions are derived? The answers are given in the examples, but I can’t figure how to get the answers they do. I’ll copy and paste the first section. If someone can tell me how problem 1. is done, I should be able to figure out 2. and 3. on my own. Thanks.
Medical Imaging/Rad Math 102

Nuclear Medicine/Radiation Therapy

Module Description: This lesson is designed to introduce the student to exposure rate constants, radiation dose versus time, distance, shielding, effective, biological and physical half-lives, and decay calculations using half-life.

Objectives: Upon completion of this module material, the student will be able to apply these concepts manually and on the calculator:

Ø Calculate exposure doses for a variety of word problems concerning changes of distance and exposure time;

Ø Apply the inverse square law to distance and radiation exposure.

Calculator: Student must utilize a Texas Instrument, model: TI-30Xa.

Topics:

Exposure Rate Constant

Radiation Dose Versus Time

Radiation Dose Versus Distance from source

Exposure Rate Constants
Principles:

The exposure rate produced by a quantity of a radioactive source can be estimated using the exposure rate constant (Γ), which is also called the gamma constant. The constant has been calculated based on the energies involved and applies only to gamma and x-ray photons.

Constants are expressed either as R• cm2/ mCi•hr at 1 cm or as μGy•m2/GBq•hr.

In order to estimate the exposure rate, you must know the constant, the activity and the distance from the source to the area of concern.

Exposure rate is expressed in units such as R/hr, mR/hr, μGy/hr.

How to calculate the exposure rate based on the gamma constant:

  X = nΓ/d2 
 Where:  X = exposure rate in units of R/hr or μGy/hr 
                      n = activity

                      Γ = exposure rate constant

                      d = distance

Remember: the units of activity and distance must match those of the gamma constant.

Examples:

  1. What is the exposure rate at 1 cm from an unshielded 20 mCi dose of Tc99m. The exposure constant is 0.59 R•cm2/mCi•hr at 1 cm.
    X R/hr = (20mCi)/(1 cm)2 X 0.59 R•cm2/mCi•hr = 11.8 R/hr or 11,800 mR/hr at 1 cm.

  2. A 6 mCi dose of Ga67 is left unshielded. If the exposure rate constant is 0.76 R•cm2/mCi•hr at 1 cm, what is the exposure rate at 10 cm?
    X R/hr = (6 mCi)/(10 cm)2 X 0.76 R•cm2/mCi•hr = 0.046 R/hr or 46 mR/hr at 10 cm

  3. What is the exposure rate from a 0.11 GBq dose of Tl201 at 1 m if the exposure constant is 12.16 μGy•m2/GBq•hr?
    X μGy/hr = (0.11 GBq)/(1m)2 X 12.16 μGy•m2/GBq•hr = 1.3 μGy/hr at 1 m.