Need help understanding volumes of cones

  • Thread starter Kirito123
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In summary, the conversation was about a person struggling to understand a math problem involving calculating volume. They provided their attempted solution and asked for clarification. The expert summarizer explains that the person was incorrectly squaring π in addition to squaring the radius, and reminds them to follow the order of operations. The person expresses understanding and thanks the expert.
  • #1
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Homework Statement


This was a example but I didn't quite understand it, I don't know how they ended up with 565.49 every time I try I get some random other number.
upload_2016-5-11_17-11-21.png

Homework Equations


upload_2016-5-11_17-11-46.png


The Attempt at a Solution


So this is how i do it.

upload_2016-5-11_17-13-52.png

Pi (6) 2 (15)/3

So first I multiply 3.14 (pi) by 6. so 3.14 x 6 = 18.84.
Now 18.84 to the power of 2 is equal to 354.9456
354.9456 x 15 = 5324.184
5324.184 / 3 = 1774.728.

I know I am wrong but i just want to know how come when i try to calculate the volume it doesn't work?
 
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  • #2
Kirito123 said:

Homework Statement


This was a example but I didn't quite understand it, I don't know how they ended up with 565.49 every time I try I get some random other number.
View attachment 100590

Homework Equations


View attachment 100591

The Attempt at a Solution


So this is how i do it.

View attachment 100592
Pi (6) 2 (15)/3

So first I multiply 3.14 (pi) by 6. so 3.14 x 6 = 18.84.
Now 18.84 to the power of 2 is equal to 354.9456
354.9456 x 15 = 5324.184
5324.184 / 3 = 1774.728.

I know I am wrong but i just want to know how come when i try to calculate the volume it doesn't work?
You are squaring π as well as squaring r.

Review ' Order of Operations '.
 
  • #3
ok i get it now, thanks alot.
 

1. What is the formula for finding the volume of a cone?

The formula for finding the volume of a cone is V = 1/3 * π * r^2 * h, where V is the volume, π is pi (approximately 3.14), r is the radius of the base, and h is the height of the cone.

2. How do you find the radius and height of a cone?

The radius of a cone is the distance from the center of the base to the edge, and the height is the distance from the base to the apex (point) of the cone. These measurements can be obtained through direct measurement or by using geometric constructions.

3. Are there any real-life applications of understanding volumes of cones?

Yes, understanding volumes of cones is important in many fields, such as engineering, architecture, and manufacturing. For example, it is used to calculate the capacity of containers, design buildings with cone-shaped roofs, and create cone-shaped objects in 3D printing.

4. How does the volume of a cone compare to the volume of a cylinder or sphere?

The volume of a cone is one-third of the volume of a cylinder with the same height and base radius. It is also smaller than the volume of a sphere with the same radius. This is because a cone has a curved surface, while a cylinder has a flat surface and a sphere is completely round.

5. Can the volume of a cone be negative?

No, the volume of a cone (or any object) cannot be negative. Volume is a measure of space and therefore, it is always positive. If you get a negative volume result, it is likely due to a calculation error.

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