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

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

Answer the following and be the brainiest the mistake in the pattern is that : a. the decimal point

Answer from: Quest

,xzgv

step-by-step explanation:

; oqirjg'

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:00, Maaarii

Fanny mendelssohn manages all the magazines and paperback books at a local grocery store. she prices many paperbacks to sell at $7.99. the cost to the store is $5.29. what is the markup rate on a paperback book, based on its cost?

Answers: 1

continue

Mathematics, 21.06.2019 18:30, BECKX6770

You love to play soccer! you make a shot at the net 8 times during a game! of those 8 attempts, you score twice. what percent of the time did you score?

Answers: 2

continue

Mathematics, 21.06.2019 19:30, kristofwr3444

Acar started driving from city a to city b, distance between which is 620 miles, at a rate of 60 mph. two hours later a truck left city b and started moving towards city a at a rate of 40 mph. how many hours after the truck's departure will the two meet?

Answers: 1

continue

Mathematics, 21.06.2019 23:30, Coolcatfurzy

Fill in the table with whole numbers to make 430 in five different ways

Answers: 1

continue

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...