Calculating Volume of a Dome - What to Measure & Equations Needed

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In summary, the conversation discusses the task of calculating the volume of a dome in a lab and transforming it into a sphere or spherical shape for thermal calculations. The speaker seeks advice on what measurements and equations to use, and is advised to establish the relationship between the base and height and use an integral. Further details on the concept of using integrals to calculate volume are provided, along with a visual representation and formula for finding the volume of a dome using the disk method. The speaker also mentions previous experience with finding volumes of different shapes using calculus knowledge.
  • #1
laminatedevildoll
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We have a dome in our lab, and my advisor asked me to calculate the its volumne and make it into a sphere or spherical. This'll be used for some thermal calculations I think. What should I measure and what equations would I need?
I'd appreciate anyone's feedback.
 
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  • #2
laminatedevildoll said:
We have a dome in our lab, and my advisor asked me to calculate the its volumne and make it into a sphere or spherical. This'll be used for some thermal calculations I think. What should I measure and what equations would I need?
I'd appreciate anyone's feedback.

Try to establish the relation between the base and height and use an integral.

Edit: Here is more detail.

First and foremost, you have to realize that in any 3d figure where the area of the base is a function of the height, we can use an integral to calculate the exact volume of the figure. If you don't already, then there is no other way.

Imagine your dome upside down (this is easier). At height 0, the base area is 0 and at maximal height, the base's area is maximal. Let's denote the maximal height by H and the maximal area of the base B. Now you need to find a function such as:

b = f(h)

and

B = f(H)

and

0 = f(0)

Where b is the area of the base and h is the height. Now to get the volume you use a simple integral:

[tex]\int_0^H \ f(h) dh[/tex]

Of course, if you don't already know these concepts, this will sound like total gebberish to you.
 
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  • #3
I'd picture it seen rotated so it's highest top is at (0,0) and it's lying on its side so the x-axis is going trough its middle. Like a cup tipped over...with the x-axis piercing its center. Then describe it by a formula. If it's a dome, I'm guessing a square root formula could work.

Then you integrate using the disk method.

Pi * Integral of f(x) * f(x) from zero to the furthest point...or the height of the dome.

I had in my 12th grade about finding volumes of different flower vases and other containers and it was very interesting I thought.

Edit: It's Calculus AB chapter "Application to integrals" knowledge.
 

FAQ: Calculating Volume of a Dome - What to Measure & Equations Needed

What is the formula for calculating the volume of a dome?

The formula for calculating the volume of a dome is V = (π * r^2 * h) / 3, where V is the volume, r is the radius, and h is the height.

What measurements are needed to calculate the volume of a dome?

To calculate the volume of a dome, you will need to measure the radius and height of the dome. These measurements can be taken using a ruler or measuring tape.

How do you measure the radius of a dome?

The radius of a dome can be measured by finding the distance from the center of the base to the outer edge of the dome. This can be done by using a ruler or measuring tape.

How do you measure the height of a dome?

The height of a dome can be measured by finding the distance from the base to the highest point of the dome. This can be done by using a measuring tape or by measuring the angle from the base to the top of the dome and using trigonometry to calculate the height.

Are there any other equations needed to calculate the volume of a dome?

No, the formula V = (π * r^2 * h) / 3 is the only equation needed to calculate the volume of a dome. However, you may also need to convert the measurements to the same units (e.g. inches or centimeters) before plugging them into the formula.

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