Math CentralQuandaries & Queries


Question from mike, a student:

A water tank has the shape of a right circular cone with height 12 feet and radius 8 feet. Water is running into the tank so that the radius r (in feet) of the surface of the water is given by r=0.75t where t is the time (in minutes) that the water has been running. the volume V of the water is given by V=1/3 pi r^2h. Find V(t) and use it to determine the volume of the water when t=5 minutes.

Hi Mike,

What you are missing is the height, h(t) of the water at time t minutes. Similar triangles helps determine this.


Triangles ABC and DEC are similar so

12/8 = h(t)/r(t).

You know that r(t) = 0.75 ft so substitute into this expression and solve for h(t). Now substitute r(t) and h(t) into the expression for the volume to determine Vt).


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