Need help understanding volumes of cones

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SUMMARY

The discussion centers on calculating the volume of a cone using the formula V = (1/3)πr²h, where r is the radius and h is the height. The user incorrectly squared π instead of the radius, leading to erroneous calculations. The correct computation for a cone with a radius of 6 and height of 15 results in a volume of approximately 565.49 cubic units. Understanding the order of operations is crucial for accurate results in mathematical calculations.

PREREQUISITES
  • Understanding of the volume formula for cones: V = (1/3)πr²h
  • Basic knowledge of the mathematical constant π (Pi)
  • Familiarity with the order of operations in mathematics
  • Ability to perform basic arithmetic operations (multiplication, squaring, division)
NEXT STEPS
  • Review the order of operations in mathematics
  • Practice calculating volumes of different geometric shapes
  • Explore the properties of π and its applications in geometry
  • Learn about common mistakes in mathematical calculations and how to avoid them
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Students studying geometry, educators teaching volume calculations, and anyone seeking to improve their mathematical problem-solving skills.

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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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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 '.
 
ok i get it now, thanks a lot.
 

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