Question

A compression wave is moving away from an explosion at 100 ft/sec. How fast is the volume within the spherical compression wave increasing in t = 4 seconds? You will need the formula for the volume of a sphere! *Leave π in your answer do not convert to a decimal!

Answer 1

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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