ok the question for my geometry class is...
Two water pipes of the same length have diameters of 6cm and 8cm. These two pipes are replaced by a single pipe of the same length, which has the same capacity as the smaller pipes combined. What is the diameter of the new pipe?
Any help would be great thanks!

2. ?

What would help is if you were to make some statements about what you already know or tried. Do you have any specific questions?

The pipes are all cylinders. Each has its own volume.

Perhaps, you're confused by the symbolism, since the fixed length for these three pipes is abstract. (Do you realize that all three pipes have the same length? That's nice because it means that we can use the same symbol while working with each pipe's volume.)

Use the formula for the volume of a cylinder, and just let the symbol L represent the length (often referred to as "height" or h, in the famous formula).

V = Pi * r^2 * L

Can you write expressions for V for each of the two pipes with known diameter?

The third pipe needs their combined volume, yes? So, add your two expressions for V together. (These two expressions are like-terms in the variable L.)

The summed expression represents the volume of the third pipe. This expression is in the form:

Pi * r^2 * L

Finish, by working backwards, to first recognize r^2, and then determine r, and then the answer is 2r.

Does this make sense, or is my description of the strategy too complicated to understand?

If you need a sample exercise, I can do that, but please try to write the volume of the two given pipes, each with length L, and show us what you get.

And, of course, feel free to ask any specific questions that might come up.

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Ok that's what i tried i just couldn't figure out how to change the volume back to diameter.
ok so my work so far has found that the smaller pipe has a volume of 9 pi h. the longer tube is 16 pi h. when i combined them i got 25 pi h. Can you show me an example of how to change it back please?
Thanks for getting back to me so soon

You can do this with Pythagoras.

$\sqrt{6^{2}+8^{2}}=$

Also, since you know the capacity of the new pipe, it's area is ${\pi}r^{2}=25{\pi}$

Solve for r and double it for the diameter of the new pipe. The length does not matter since it will cancel anyway, and they are asking for capacity.

5. ?

Originally Posted by sbsbsbsbsb

Ok that's what i tried i just couldn't figure out how to change the volume back to diameter.

Why did you not simply say so, at the beginning?
V = Pi * r^2 * h

V = Pi * 25 * h

When we compare your result to the volume formula above it, I think it's clear that r^2 is 25, for the third pipe.

Do you "see" that?

So, if we know r^2 = 25, it is very easy to calculate r. Just take the square root.

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ok that make sense!! Thank you SOOO much!......mmm4444bot i thought i was completely off so thats why i didnt post what i already had

ok i another question....so you are given that there is a right square prism a with a base edge of 9 and volume of 891. How would i get the height? When i tried it i got 24.75 is that right?

Originally Posted by sbsbsbsbsb
ok i another question....so you are given that there is a right square prism a with a base edge of 9 and volume of 891. How would i get the height? When i tried it i got 24.75 is that right?
What equation did you use for volume of the prism?

the volume was given

10. ?

Subhotosh understands that the volume is given.

He's asking you to show us the formula for the volume of a right square prism because (1) you need to use the formula to find the height, and (2) we want to be sure that you know the correct formula.

I'll show you how we find the height, with an example that involves the volume of a different object.

A tall cylindrical water tank has a radius of 7 meters and a volume of 980*Pi cubic meters. What is its height?

We use the formula for the volume of a cylinder, and substitute in the two given values.

V = Pi * r^2 * h

980 Pi = Pi * (7)^2 * h

980 Pi = Pi * 49 * h

Now, we solve for h.

(980 Pi)/(49 Pi) = h

h = 980/49

h = 20

The water tank is 20 meters high.

You need to follow the same strategy. Substitute the given values into the formula for the volume of a right square prism, and solve for h.

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