A tank of water in the shape of a cone


Asked by wiki @ in Physics viewed by 761 People


A tank of water is in the shape of a cone (assume the ""point"" of the cone is pointing downwards) and is leaking water at a rate of 35 cm3/sec. The base radius of the tank is 1 meter and the height of the tank is 2.5 meters. When the depth of the water is 1.25 meters at what rate is the (a) depth changing and (b) the radius of the top of the water changing?\

Answered by wiki @



Answer:

a) dh/dt = -44.56*10⁻⁴ cm/s

b) dr/dt = -17.82*10⁻⁴ cm/s

Explanation:

Given:

Q = dV/dt = -35 cm³/s

R = 1.00 m

H = 2.50 m

if h = 125 cm

a) dh/dt = ?

b) dr/dt = ?

We know that

V = π*r²*h/3

and

tan ∅ = H/R = 2.5m / 1m = 2.5  ⇒ h/r = 2.5

⇒  h = (5/2)*r

⇒  r = (2/5)*h

If we apply

Q = dV/dt = -35 = d(π*r²*h/3)*dt

⇒  d(r²*h)/dt = 3*35/π = 105/π   ⇒   d(r²*h)/dt = -105/π

a) if   r = (2/5)*h

⇒  d(r²*h)/dt = d(((2/5)*h)²*h)/dt = (4/25)*d(h³)/dt = -105/π

⇒  (4/25)(3*h²)(dh/dt) = -105/π

⇒  dh/dt = -875/(4π*h²)

b) if  h = (5/2)*r

Q = dV/dt = -35 = d(π*r²*h/3)*dt

⇒  d(r²*h)/dt = d(r²*(5/2)*r)/dt = (5/2)*d(r³)/dt = -105/π

⇒  (5/2)*(3*r²)(dr/dt) = -105/π

⇒  dr/dt = -14/(π*r²)

Now, using h = 125 cm

dh/dt = -875/(4π*h²) = -875/(4π*(125)²)

⇒  dh/dt = -44.56*10⁻⁴ cm/s

then

h = 125 cm  ⇒  r = (2/5)*h = (2/5)*(125 cm)

⇒  r = 50 cm

⇒  dr/dt = -14/(π*r²) = - 14/(π*(50)²)

⇒  dr/dt = -17.82*10⁻⁴ cm/s


Do you know the better answer?

Similar Questions

Which is the best strategy for avoiding long term stress

Asked by wiki @ in Health viewed by 227 persons

Which is the best strategy for avoiding long-term stress? A. Develop a fun hobby and spend time on it every day. B. Manage time effectively and include time to relax. …

How did the creation of israel affect the middle east

Asked by wiki @ in History viewed by 177 persons

How did the establishment of Israel affect the Middle East?

Which of the following statements is true of cardiovascular disease

Asked by wiki @ in Health viewed by 126 persons

10. Which of the following statements about cardiac arrest is true? Cardiac arrest is the same as a heart attack. A person who is in cardiac arrest is not responsive, …

Which of the following statements is true about learning disability

Asked by wiki @ in Computers and Technology viewed by 208 persons

Which of the following statements are true regarding cognitive impairments? Select 3 options. To improve cognitive accessibility, the developer should focus on a clear and consistent design. Speech input devices …

In the following sentence which word is the abstract noun

Asked by wiki @ in English viewed by 252 persons

In the following sentence, which word is the abstract noun? Quincy insisted that each one of his team members demonstrate loyalty. A. Quincy B. loyalty C. members D. team

An enzyme can only bind one reactant at a time.

Asked by wiki @ in Biology viewed by 92 persons

An enzyme can only bind one reactant at a time.                 A)           True                 B)            False

El empleado busca la reservación

Asked by wiki @ in Spanish viewed by 256 persons

Place these events in order based on the Fotonovela video. El empleado busca la reservación. Marissa dice que está confundida. Los amigos están listos para ir a la playa. El …

Why did many conservatives disagree with new deal economic policies

Asked by wiki @ in History viewed by 298 persons

Why did many conservatives disagree with New Deal economic policies? Many conservatives believed in balanced budgets, low taxes, and low government spending. Many conservatives believed a deficit would eventually lead …

The work in process inventory account of a manufacturing corporation

Asked by wiki @ in Business viewed by 204 persons

The work in process inventory account of a manufacturing corporation shows a balance of $18,000 at the end of an accounting period. the job cost sheets of the two uncompleted …

What did the tet offensive show the american people apex

Asked by wiki @ in History viewed by 88 persons

What did the Tet Offensive show the American people? A. It seemed to prove that America was not winning in Vietnam. B. It proved that the Vietnamese army was too …

How do authors use narrative elements to create a story

Asked by wiki @ in English viewed by 203 persons

How do authors use narrative elements to create a story

What is the focal point on a plate of food

Asked by wiki @ in Spanish viewed by 242 persons

Which of the following is usually the focal point of the plate? Main itemC. Sauces.. GarnishesD. RelishesThis plating approach uses odd numbers and negative space.1. …

A sharp rise in the real value of stock prices

Asked by wiki @ in Business viewed by 197 persons

A sharp rise in the real value of stock prices, which is independent of a change in the price level, would best be an example of: A. The interest-rate effect …

Why is it hard to make a good flu vaccine

Asked by wiki @ in English viewed by 196 persons

Why is it hard to make a good flu vaccine? A) Vaccines take months to make, so people have to guess which strains of flu are going to be active …

Why does australia have such an unusual variety of spiders

Asked by wiki @ in Biology viewed by 79 persons

Why does Australia have such an unusual variety of spiders?

Describe surface tension in a group of bonded water molecules

Asked by wiki @ in Biology viewed by 260 persons

Describe surface tension in a group of bonded water molecules

How many gallons of paint for 1300 sq ft house

Asked by wiki @ in Mathematics viewed by 251 persons

The front of a house needs to be painted black. The garage door is 1.5 m high and 2 m wide. A) How many square meters of black paint will …

Which tactic did palestinians use against israel in 1987

Asked by wiki @ in History viewed by 221 persons

Which tactic did Palestinians use against Israel in 1987?

Meaning of the song don t stop believing by journey

Asked by wiki @ in Arts viewed by 198 persons

In Dont Stop Believing -Journey's Do the lyrics contain any examples of stereotyping? Do you feel the music supports the song’s text?

What are the two types of primary safeguarding methods

Asked by wiki @ in Computers and Technology viewed by 227 persons

What are the two types of primary safeguarding methods Select two options that apply A- types B- guards C- devices D- pictorial

17 5 as a mixed number

Asked by wiki @ in Mathematics viewed by 190 persons

What is 17/5 as a mixed number in simplest form?

Which economic indicators are used to measure the global economy

Asked by wiki @ in Business viewed by 228 persons

Which economic indicators are used to measure the global economy? Check all that apply. purchasing power parity trade volumes spending power parity labor market data gross domestic product trade deficits …

Which event brought thousands of people to california in 1849

Asked by wiki @ in History viewed by 242 persons

Which event brought thousands of people to California in 1849? A. job fair B. suffrage convention C. centennial exposition D. gold rush pls hurry i will mark you the brainlyest

Which of the following can increase your credit cards apr

Asked by wiki @ in Business viewed by 229 persons

Which of the following can increase your credit cards APR a. Paying the minimum b. Missing a credit card payment c. Paying off the full balance d. Cashing in on …

What are three types of muscles in the human body

Asked by wiki @ in Health viewed by 228 persons

List the three types of muscles that are found in the human body Lo 2

What is the use of mortar and pestle in laboratory

Asked by wiki @ in Chemistry viewed by 143 persons

In the chemical laboratory, what does a mortar and pestle function as?. . a.to increase surface area of a solute. . b.to decrease surface area of a solute. . c.to …

How did european nations come to rule most of africa

Asked by wiki @ in History viewed by 202 persons

How did European nations come to rule most of Africa, despite the presence of strong African kingdoms? A) The Europeans had superior weapons B) The Europeans convinced Africans that their …

Which items in the list are methods a political party

Asked by wiki @ in History viewed by 202 persons

Which items in the list are methods a political party might use to influence public opinion? O A. A and C only O B. B and C only O C. …

What is the power source that drives the water cycle

Asked by wiki @ in Chemistry viewed by 204 persons

How is the sun the major source of energy in the water cycle? Group of answer choices It provides the energy to condense atmospheric water vapor into rain. It provides …

In which register is the narrator's voice in schubert's elrkõning

Asked by wiki @ in History viewed by 97 persons

in which register is the narrators voice in schuberts "Elrkõning"? A one of the highest B the softest C the loudest D a neutral one

Most viewed questions in Physics


A 0.25 kg arrow with a velocity of 12m s

Asked by wiki @ in Physics viewed by 937 persons


Uranium 235 undergoes an alpha decay to produce thorium 231

Asked by wiki @ in Physics viewed by 918 persons


Water waves in a small tank are 06 m long

Asked by wiki @ in Physics viewed by 827 persons



A golf club hits a stationary 0.050 kilogram golf ball

Asked by wiki @ in Physics viewed by 810 persons


In which electric circuit would the voltmeter read 10 volts

Asked by wiki @ in Physics viewed by 761 persons


A tank of water in the shape of a cone

Asked by wiki @ in Physics viewed by 760 persons



A 90 kg person rides a spinning amusement park ride

Asked by wiki @ in Physics viewed by 738 persons


The initial speed of a cannonball is 0.20 km s

Asked by wiki @ in Physics viewed by 737 persons


How many times does your heart beat during your lifetime

Asked by wiki @ in Physics viewed by 737 persons



A 60 kilogram student jumps down from a laboratory counter

Asked by wiki @ in Physics viewed by 715 persons


All of the following are advantages of outsourcing except it

Asked by wiki @ in Physics viewed by 697 persons


A 5.8 x 10 4 watt elevator motor can lift

Asked by wiki @ in Physics viewed by 676 persons



A golfer hits a ball at an angle of 25

Asked by wiki @ in Physics viewed by 667 persons


7 types of electromagnetic waves from lowest to highest frequency

Asked by wiki @ in Physics viewed by 607 persons


Which of the following statements about diffusion is true

Asked by wiki @ in Physics viewed by 585 persons