Mathematics, 25.03.2020 00:52 giavanleer14

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the water changing when the height is 3m?

Answers: 1

Show answers

Answers

Answer from: jslaughter3

The height of the water is changing at a rate of approximately 0.318 meters per second.

The volume formula of the cylinder (), in cubic meters, is described below:

$V = \pi\cdot r^{2}\cdot h$ (1)

Where:

- Radius of the cylinder, in meters.

- Height of the cylinder, in meters.

According to the statement, the leakage is represented by a decrease in the height of the water. By differential calculus and under the assumption that no rate of change exists for the radius, we have the expression for the rate of change in the height of the water within the cylinder ( $\dot h$ ), in meters per second:

$\dot h = \frac{\dot V}{\pi\cdot r^{2}}$ (2)

Where $\dot V$ is the rate change in the volume occupied by the water, in cubic meters per second.

If we know that $\dot V = 4\,\frac{m^{3}}{s}$ and $r = 2\,m$ , then the rate of change in the height is:

$\dot h = \frac{4\,\frac{m^{3}}{sec} }{\pi\cdot (2\,m)^{2}}$

$\dot h \approx 0.318 \,\frac{m}{s}$

The height of the water is changing at a rate of approximately 0.318 meters per second.

We kindly invite to check this question on rates of change: link

Answer from: heatherballiet866

Therefore the rate change of height is $\frac{1}{\pi}$ m/s.

Step-by-step explanation:

Given that a vertical cylinder is leaking water at rate of 4 m³/s.

It means the rate change of volume is 4 m³/s.

$\frac{dV}{dt}=4 \ m^3/s$

The radius of the cylinder remains constant with respect to time, but the height of the water label changes with respect to time.

The height of the cylinder be h(say).

The volume of a cylinder is $V=\pi r^2 h$

$=( \pi \times 2^2\times h)\ m^3$

$\therefore V= 4\pi h$

Differentiating with respect to t.

$\frac{dV}{dt}=4\pi \frac{dh}{dt}$

Putting the value $\frac{dV}{dt}$

$\Rightarrow 4\pi \frac{dh}{dt}=4$

$\Rightarrow \frac{dh}{dt}=\frac{4}{4\pi}$

$\Rightarrow \frac{dh}{dt}=\frac{1}{\pi}$

The rate change of height does not depend on the height.

Therefore the rate change of height is $\frac{1}{\pi}$ m/s.

Answer from: Quest

Bis your answer. it only holds the decimal numerals
Which of the following is not a possible value for a probability?

Answer from: Quest

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41 $4.41/7 = $.63 each at fresh side

5 bagels for $3.60 $3.60/5 = $.72 each at value mart

Another question on Mathematics

Mathematics, 21.06.2019 17:30

Noor brought 21 sheets of stickers. she gave 1/3 of a sheet to each of the 45 students at recess. she wants to give teachers 1 1/2 sheets each.

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

The areas of two similar triangles are 72dm2 and 50dm2. the sum of their perimeters is 226dm. what is the perimeter of each of these triangles?

Answers: 1

Answer

Mathematics, 22.06.2019 00:00

30 points! here is a you are the new manager at trusty goods wholesale produce. you need to figure out how to adjust the amount of produce in your notes after the events of the day: you got 5 more crates of bananas someone returned 2 crates of apples a worker dropped a crate of grapes (oh no! , you had to throw them out) you sold a crate of bananas you sold 5 crates of apples can you write an expression to describe your day using: "a" for crates of apples "b" for crates of bananas and "g" for crates of grapes? make sure the expression is in simplest form question 2 (3 points) explain your steps using sentences.

Answers: 2

Answer

Mathematics, 22.06.2019 04:20

Atriangle abc has two side lengths of 28 ft. and 24 ft. if angle c is 91°, what's the measurement of angle b?

Answers: 1

Answer

You know the right answer?

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a...

Questions