2017年7月11日 · A surface integral needs two parameters although the surface element vector needs three components. We can write those components in cartesian coordinates and the surface parameters can be adopted from the description in cylindrical coordinates.

2019年11月14日 · The issue is that you assumed an INVERTED cone, which I can tell because you used $(4-x)^2$ instead of $\displaystyle \frac{x^2}{16}$. The base of the cone is at top! I'm not sure what you mean by pumping to a spot two feet above the top of the cone, but it would be multiplying the integral (perhaps $\displaystyle \int_4^6$ cone) by the density ...

2016年3月10日 · A water tank in the form of an inverted cone is being emptied at the rate of $6$ ft$^3$/min. The altitude of the cone is $24$ ft, and the base radius is $12$ ft. Find how fast the water level is lowering when the water is $10$ ft deep. I am not how to do this problem, but I've tried this using the volume formula for cone:

2020年5月6日 · “A tank has the shape of an inverted circular cone with a radius of 2 feet and a height of 5 feet. If the tank contains gasoline to a death of 1 foot, find the work required to empty the tank through the pipe extending 1 feet above the top of the tank.” Use y as the weight for the gasoline . I have no idea to go about this.

2020年2月8日 · pumping water out of inverted circular cone. 1. Rate of change volume of a cone. 23.

2021年2月27日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2015年2月16日 · "A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone would the liquid rise?" That's it. No other numbers specified. Any help would be appreciated. Thanks.

2009年5月31日 · A tank has the shape of an inverted circular cone with height H=10m and base radius R=2m. The tank is initially full of water. Find the work required to lower the height of the water level to h=6m by pumping the water to the top of the tank. The density of water is r = 1000 kg/m3 and the acceleration due to gravity is g = 9.8 m/s2.

2020年10月21日 · "A cone-shaped tank is mounted vertically with its pointed end down. It has a height of 10 m and a radius of circular base 5 m. Water flows at a rate of 8m^3 / min. How fast does the water level rise when the water is 5 m high? I calculated tanu=5/10=0,5, where u is the angle between the height h=10 and the side of the cone.

Water is poured into an inverted cone at a rate of π-units per second. If the radius of the base of the cone is r and its height is 2r, what is the rate at which the depth of the water is changing when the height of the water is 1/2r?