Related Rates: water in tank, triangle height, balloon

[noselord]

Can anyone help me out with these questions? I'm so lost in this unit... lol I have 3 questions left and I really need help on them.

1. Water runs into a tank that is in the shape of an inverted cone at the rate of 9cubic feet/min. The tank has a height of 10 ft and a base radius of 5 ft. How fast is the water level rising when the water is 4 ft deep?

2. The length of the base of a right triangle is increasing at the rate of 12in/min. At the same time, the height of the triangle is decreasing in such a way that the length of the hypotenuse remains 10 inches. How quickly is the height of the triangle changing when the length of the base is 6 inches?

3. A spherical balloon is being inflated so that its volume is increasing at the rate of 5 cubic meters/min. At what rate is the diameter increasing when the diameter is 12m? (V = 4/3(pi)r^3)

Thanks in advance!

 

[Deleted member 4993]

Re: Related Rates Problems Please Help!!!

Can anyone help me out with these questions? I'm so lost in this unit... lol


I have 3 questions left and I really need help on them.


Water runs into a tank that is in the shape of an inverted cone at the rate of 9cubic feet/min. The tank has a height of 10 ft and a base radius of 5 ft. How fast is the water level rising when the water is 4 ft deep?

The length of the base of a right triangle is increasing at the rate of 12in/min. At the same time, the height of the triangle is decreasing in such a way that the length of the hypotenuse remains 10 inches. How quickly is the height of the triangle changing when the length of the base is 6 inches?

A spherical balloon is being inflated so that its volume is increasing at the rate of 5 cubic meters/min. At what rate is the diameter increasing when the diameter is 12m? (V = 4/3(pi)r^3)

Thanks in advance!

Duplicate post

http://www.sosmath.com/CBB/viewtopic.ph ... 169#155169

Please show us your work - and exactly where you are stuck - so that we know exactly where to start.

 

[noselord]

Re: Related Rates Problems Please Help!!!

i think i got the answers

could u double check please?

In order

1) 9/4(pi)
2) -3/4
3) 5(pi) / 72

 

[Deleted member 4993]

Re: Related Rates Problems Please Help!!!

i think i got the answers

could u double check please?

In order

1) 9/4(pi)
2) -3/4
3) 5(pi) / 72

The correct answers will have units associated with it - so those are wrong.

Again, show your work....

 

[tkhunny]

You're not getting the idea.

1) SHOW YOUR WORK! Just the answer is NOT good enough.

2) Don't EVER post the same problems in different places. Volunteers works on these things. Generally, you need only one answer. If you get two that are substantially the same, you have wasted the time of at least one of the volunteers. We don't want to waste the time of even a single volunteer. We make the world a better place when we volunteer to help people. Do you REALLY want to discourage that?

3) Did I mention that you need to show your work? I think I did.

 

[stapel]

To get you started...

1. Water runs into a tank that is in the shape of an inverted cone at the rate of 9cubic feet/min. The tank has a height of 10 ft and a base radius of 5 ft. How fast is the water level rising when the water is 4 ft deep?

Draw the inverted cone in "side view", so it's an upside-down isosceles triangle. Label the (fixed) height and radius. Draw the vertical line from the base (on top) to the vertex (at the bottom) indicating the full height, thus splitting the triangle into two right triangles.

Draw a horizontal line through the cone somewhere in the middle, indicating the (changing) height of the water. Note that you now have nested (and thus similar) triangles. Use this information to express r in terms of h, and also to find the radius r for h = 4.

Take the formula for the volume V of a right circulular cone with height h and radius r. Substitute your expression for r (in terms of h), so you have the volume expressed in terms of only V and g. Differentiate with respect to time t. Note that you are given that dV/dt = 9. Plug in the given value for h and the obtained value of r. Solve for the numerical value of dh/dt.

Note the units of time and linear measure, and put the correct units on the numerical answer. (Your formatting is ambiguous. You may be nearly done on this one.)

2. The length of the base of a right triangle is increasing at the rate of 12in/min. At the same time, the height of the triangle is decreasing in such a way that the length of the hypotenuse remains 10 inches. How quickly is the height of the triangle changing when the length of the base is 6 inches?

Draw the right triangle with the right angle at the origin, the base on the x-axis, and the height on the y-axis. (This is for simplicity's sake.) You can relate the lengths of the sides using the Pythagorean Theorem. Use the Theorem to find the height y when the base is x = 6. (The hypotenuse, of course, is always equal to 10.)

Returning to the Theorem, differentiate with respect to time t. Plug in the given value for the base, the found value for the height, the given value for the hypotenuse, and the given value for dx/dt, noting that the hyptenuse is fixed, so the derivative of that term will be zero. Solve for the numerical value of dy/dt.

Note the units of time and linear measure, and put the correct units on the numerical answer. (My answer differs from what you have posted.)

3. A spherical balloon is being inflated so that its volume is increasing at the rate of 5 cubic meters/min. At what rate is the diameter increasing when the diameter is 12m? (V = 4/3(pi)r^3)

Note that the diameter d is related to the radius r by d = 2r. Use this to express the volume V in terms of the diameter, and differentiate with respect to time t.

Plug in the given values for d and dV/dt, and solve for the numerical value of dd/dt.

Note the units of time and linear measure, and put the correct units on the numerical answer. (I believe you're almost done with this one.)

Eliz.