When calculating the volume of a solid when revolving on either axis, if a particular axis is not given within the question, how does one figure on which axis the function is revolving around?

A container in the shape of an inverted right cone of radius 2 cm and depth 5 cm is being filled with water. When the depth of water is h cm, the radius of the water is r cm A. Use similar triangles to express r in terms of h. B. Express the volume of the water as a function of h. C. At what rate with resepct to the depth of water is the volume of water changing when its depth is 1 cm?

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 12 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 2 feet high? (Hint: The formula for the volume of a cone is V = {mr?h.)

A conical container, with its axis vertical and vertex downwards, is full of water. The water is emptying through a small hole at the vertex. If the depth of water after 1 minutes is h cm, and the rate at which the volume of water flows out is proportional to √h, show that -kh-3/2, where k is a positive constant. dh di

At the bottom of a swimming pool, the pressure exerted at a given point is proportional to the depth of the water above it. In particular, the pressure at a given point of depth d is equal to 10, 000d Pascals. We will investigate the total pressure at the bottom of a swimming pool depending on its shape. You may view 3D models of the swimming pools for reference here (note that this is one model plotting the depth as a function of x and y, so represents essentially the pool flipped upside-down): https://www.geogebra.org/m/nnf4yhax (a) Suppose we have a rectangular pool that is 50 meters long and 25 meters wide. The pool has a shallow end that is 1 meter deep at the edge, a deep end 50 meters away that is 3 meters deep at the edge, and is such that the bottom of the pool forms a linear slant in between (so along a line segment parallel to the short side, the pool has constant depth, and along a line segment parallel to the long side, the pool's depth varies linearly). Set up and…

Complete the table with this data. Show solutions