3. SN 1987A, which occurred in the LMC (50 kpc away), is thought to have produced 1058 neutrinos. Kamiokande II, which had 1000 detectors, each with a radius of 0.25 m, detected 12 of those neutrinos.
(a) What is the total area of a sphere extending from the LMC to Earth?
(b) What was SN 1987A’s neutrino flux at the Earth? (Flux is defined as number of neutrinos per area = neutrinos per square meter.)
(c) What is the total collecting area of the 1000 Kamiokande II detectors?
(d) How many SN 1987A neutrinos passed through the Kamiokande II detectors?
(e) What was the efficiency of Kamiokande II? (Fraction of the neutrinos entering the detectors actually detected.)
A = 4pi(r)^2
V= 4/3 * pi(r)^3
Assuming that this sphere has a radius of 50kpc, I've converted to m (1.543e21) and plugged into the area equation for a total area of 2.992e43 m^2. From here I've talked myself into circles, and I honestly don't know where to go next. Any help or guidance would be greatly appreciated!