On October $21,2001,$ Ian Ashpole of the United Kingdom achieved a record altitude of $3\mathrm{.}35$ km $(11,000$ ft$)$ powered by $600$ toy balloons filled with helium. Each filled balloon had a radius of about $0\mathrm{.}55$ m and an estimated mass of $0\mathrm{.}29$ kg$.$

$($a$)$ Estimate the total buoyant force on the $600$ balloons. $($Enter your answer to at least two decimal places.$)$

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$($b$)$ Estimate the net upward force on all $600$ balloons.

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$($c$)$ Ashpole parachuted to Earth after the balloons began to burst at the high altitude and the system lost buoyancy. Why did the balloons burst?

Atmospheric pressure at this $---$Select$---$high$$low altitude is much $---$Select$---$lower$$higher than at the Earth's surface.