A solid right circular cone of height h with a 90° vertex angle has density at point P numerically equal to the distance from P to the central axis of the cone. Choosing the placement of the cone which will give the easiest integral, find its mass.

how can the mass of a solid can be found using triple integrals in rectangular coordinates?

Two spherical tanks are connected as in the figure below. The first tank has the radius 1m and is on the ground. The bottom of the second tank is located 2m above the top of the first tank. The second tank has the radius 0.5m. Two tanks are connected by a tube of negligible width that is going through the top of the first tank and the bottom of the second tank. Let p > 0 be the density (in kg/m^3) of the liquid in both tanks. Find the work required to deliver the liquid to fill both tanks from the ground. 2

The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region 0.6x² and below the line 2 above the curve y y = 280. (Here, distances are measured in meters.) The water level is 34 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by kg m³ = water pressure. (Water has a density of 1000- and the acceleration of gravity is 9.8 m sec² .) " Note: Weight density of water is 1000 (9.8)=9800 N/m^3

A tank, shaped like a cone has height 8 meters and base radius 3 meters long. It is placed so that the circular part is upward. It is full of water, and we have to pump it all out by a pipe that is always leveled at the surface of the water. Assume that a cubic meter of water weighs 10000N, i.e. the density of water is 10000- . How much work does it require to pump all water out of the tank? N m³ Enter the exact value of your answer. W || Joules