Volume Displacement in a Cylinder and Cone

A cylindrical water tank has a radius of 5 meters and a height of 10 meters. The tank is filled with water to a height of 8 meters. A conical filter with a radius of 3 meters and a height of 6 meters is lowered into the tank for cleaning the water. The volume of water displaced by the conical filter affects the height of the water in the tank. What will be the new height of the water in the tank after the filter is submerged?

Recall that the volume V of a cylinder can be calculated using the formula: $$V = ext{Base Area} \times ext{Height}$$ where the Base Area for a cylinder is obtained using the formula: $$A = \\pi r^2$$. For a cone, the volume is given by: $$V = \f\frac{1}{3} \pi r^2 h$$.