Use spherical coordinates to find the volume of a ball with radius R(in other words, use spherical coordinates to prove the volume formula V =4πR^3/3)

A glass tunnel in the shape of a half cylinder with length 58 feet and radius 7 feet is built along the bottom of an aquarium that is 43 feet deep. Set up an integral that would find the fluid force on the tunnel (water density = 62.5 lbs/ft³) Force = 1₁ -7 dx

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