Calculating radius of cone - Only area of 123081 and volume of 2462940 are given

[Ward]

Hello all

I've been trying to solve this question for quite a while, but neither my father, my brother nor the internet has been able to help me out. The question? I have to calculate the radius and the height of a cone, solely knowing its area and volume.

A cone has an area of 123081 and a volume of 2462940. Calculate its height and its radius.

I would be so thankful for anyone who is willing to solve this or explain it to me. Thanks in advance! :]

 

[Deleted member 4993]

Hello all

I've been trying to solve this question for quite a while, but neither my father, my brother nor the internet has been able to help me out. The question? I have to calculate the radius and the height of a cone, solely knowing its area and volume.

I would be so thankful for anyone who is willing to solve this or explain it to me. Thanks in advance! :]

What are the formulae for:

Area of cone

Volume of cone

 

[stapel]

I have to calculate the radius and the height of a cone, solely knowing its area and volume.

A cone has an area of 123081 and a volume of 2462940. Calculate its height and its radius.

How is your book defining the "area" of the three-dimension figure? I mean, they must intend "area" to mean "surface area", but are they including only the slanty parts, or also the base?

I've been trying to solve this question for quite a while...

Great! Please show us what you've tried so far! This will help us understand what is being asked, and where you're getting stuck. Thank you!

 

[Ward]

What are the formulae for:

Area of cone

Volume of cone

The formula for the area would be r² * pi + pi * r * l
For the volume, 1/3 * pi * r² * h

How is your book defining the "area" of the three-dimension figure? I mean, they must intend "area" to mean "surface area", but are they including only the slanty parts, or also the base?

I'm not too sure as to what they consider the area, but I suppose the base is included as that would be more correct. I'm not solving math problems in a book or for school -and I haven't seen this in school yet (15 y/o, Belgium)- I'm actually trying to solve a mystery cache for Geocaching. The height of this cone will be between 100 and 999, as I need three ciphers that represent ABC. The radius should be between 10 and 99, as that would give me DE.

Great! Please show us what you've tried so far! This will help us understand what is being asked, and where you're getting stuck. Thank you!

I actually have got not clue on how to start this, because there's just so little information, but others have managed to get it right, so it must be possible. I started with transforming the formulae, which became this... VVV

2462940 = 1/3 * 3.14 * r * r * h
3 * 2462940/3.14 = r * r * h
2.353.127 = r * r * h
2.353.127/h = r * r

123081 = 3.14 * r * r + 3.14 * r * l
123081 - 3.14 * r * l = 3.14 * r * r
(123081 - 3.14 * r * l )/3.14 = r * r

So, [2.353.127/h] and [(123081 - 3.14 * r * l )/3.14] would be equal to each other, as they are both r²

This isn't how I will solve it, is it?