💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Water is leaking out of an inverted conical tank at a rate of $ 10,000 cm^3/min $ at the same time that water is being pumped into the tank at a constant rate. The tank has height $ 6 m $ and the diameter at the top is $ 4 m. $ If the water level is rising at a rate of $ 20 cm/min $ when the height of the water is $ 2 m, $ find the rate at which water is being pumped into the tank.

$$289.253 \mathrm{cm}^{3} / \mathrm{min}$$

03:06

Wen Z.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

University of Nottingham

Idaho State University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

07:00

Two tanks A conical tank w…

08:16

A conical tank has height …

03:32

A cylinder is leaking wate…

01:23

For the following exercise…

04:59

- A draining conical reser…

03:15

Filling a hemispherical ta…

05:14

A tank is shaped like an u…

05:23

Water flows into a conical…

01:14

08:58

Draining Conical Reservoir…

in order to secure up the rate at which the water is being pumped. We have to recall the volume of a cone is pi r squared times h over three. You know, 1/3 h. So let's plug in what we know. Remember ours h over three. Therefore, we have pi times h over three square exists pi r squared times h over three which gives us high over 27 cause three scores nine men times three is 27 h cubed which gives us Devi over. DT is pi over nine page squared times D h over DT. So some are taking the derivative, as you can see which gives us P minus 10,000 equals high over nine times 200 squared times 20 which simplifies to 2.89 times 10 to the fifth centimeters cubed per minute is our unit for this rate here

Numerade Educator

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Two tanks A conical tank with an upper radius of $4 \mathrm{m}$ and a height…

A conical tank has height 3 $\mathrm{m}$ and radius 2 $\mathrm{m}$ at the to…

A cylinder is leaking water but you are unable to determine at what rate. Th…

For the following exercises, consider a right cone that is leaking water. Th…

- A draining conical reservoir Water is flowing at the rate of$50 \mathr…

Filling a hemispherical tank A hemispherical tank with a radius of $10 \math…

A tank is shaped like an upside-down square pyramid, with base of $4 \mathrm…

Water flows into a conical tank with cross-sectional area $\pi x^{2}$ at hei…

Draining Conical Reservoir Water is flowing at the rate of 50 $\mathrm{m}^{3…