Long calculation problem $(10$ marks$)$

A gravimeter placed on a plane measured the gravitational attraction of water masses in a lake,

which has a shore with a circular shape and radius $150$ km $.$ The depth of the lake is $300$ m $.$ In a

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gravity survey in the following year, the water level dropped by $40$ m $.$ Can the gravimeter record

the change in the gravitational attraction of the lake water masses if the sensitivity of the

instrument is $0\mathrm{.}1$ mGal and the plane altitude in both surveys is $800$ m $?$ You can disregard the

kinematic acceleration of the plane. Sketch the problem. Use an appropriate mathematical

approximation of the lake's volume.