How Do You Calculate Total Alpha-Decays in Radium-226 Experiment?

[sparkle123]

Homework Statement

It is found that when a 6.3 x 10–5 g sample of radium-226 is placed in a vacuum and exposed
to a screen of area 1.0 mm2 placed 1.5 m away from the sample, an average of 46 α-particles
hit the screen in 10.0 minutes. Calculate the total number of decays per gram of radium-226 per
second.


2. Solution provided

α−particles emitted by 63 μg in 10 min & hitting screen = 46
thus α−particles emitted by 1 g in 1 min & hitting screen = 46/(10×60) × 1/(6.3×10−5) =1.2 ×10^3
total α−particles emitted by 1 g in 1 min = 46/(10×60) × 1/(6.3×10−5) × 4 π (1.5 ×10^3)^2
= 3.4 ×10^10 g-1 s-1

I don't understand where "4 π (1.5 ×10^3)^2" comes from. Please explain?

Thanks!

 

[gneill]

Assume that the radium emits particles equally in all directions. The screen only sampled a 1 millimeter square area. What's the total potential surface area at the sampling distance?