$5.$ One of the largest sounds in recent history was that made by the explosion of Krakatoa Volcano on August $26-27,1883.$ According to barometric pressure measurements, the sound had a decibel level of $180$ dB at a distance of $161$ km$.($a$)$ Assuming the intensity falls off as the inverse of the distance squared $($i$.$e$.$ no reflection or absorption of sound occurs$)$ what was the decibel level on Rodriguez Island $4800$ km away? $($b$)$ Since $130$ dB is generally accepted as the threshold of pain, calculate the radius around the volcano where the sound was so loud that it caused pain to those who heard it$.$