The volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.
Volume of a sphere
Given:
dr/dt=100 ft/sec
When: t=4 seconds, radius(r)=400ft
Hence:
Volume of a sphere (V)=4/3πr³
dv/dt=4/3π.3r² dr/dt
dv/dt=4πr²dt/dr
When t=4 seconds
dv/dt=4π×(100×4)²×100 cubic ft/sec
dv/dt=4π×(400)²×100 cubic ft/sec
dv/dt=64000000π cubic ft/sec
Therefore the volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.
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