Figuring out the radius of a sphere, using only the volume

Xentus

Xentus

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So basically here's the problem :

Calculate the radius of a sphere with a volume of 1.73m3 (correct to 1 decimal place)

So far I know how to get the volume of a sphere with using either diameter, or radius, 4/3πr3 but I can't seem to figure out how to get the answer with just the volume, so far I've tried "reverse-engineering" the problem, like saying 1.73 cube-root = 1.200, but that didn't work. I also tried removing π from 1.73, but that didn't help either. If my attempts seem stupid and pathetic, that's because I'm horrible at math, and equation-solving so pardon me for my knowledge.
 
Last edited:
Xentus said:
So basically here's the problem :

Calculate the radius of a sphere with a volume of 1.73m3 (correct to 1 decimal place)

So far I know how to get the volume of a sphere with using either diameter, or radius, 4/3πr3 but I can't seem to figure out how to get the answer with just the volume, so far I've tried "reverse-engineering" the problem, like saying 1.73 cube-root = 1.200, but that didn't work. I also tried removing π from 1.73, but that didn't help either. If my attempts seem stupid and pathetic, that's because I'm horrible at math, and equation-solving so pardon me for my knowledge.[/math]
Click to expand...
Since we are given the volume and you know the formula, you get the following equation:
1.73 = 4/3πr3
Can you solve it for r?
If not, how about 8 = 4*x? Can you solve it for x?
 
lev888 said:
Since we are given the volume and you know the formula, you get the following equation:
1.73 = 4/3πr3
Can you solve it for r?
If not, how about 8 = 4*x? Can you solve it for x?
Click to expand...
What's x? Volume? Radius? or is it unknown
 
Xentus said:
So basically here's the problem :

Calculate the radius of a sphere with a volume of 1.73m3 (correct to 1 decimal place)

So far I know how to get the volume of a sphere with using either diameter, or radius, 4/3πr3 but I can't seem to figure out how to get the answer with just the volume, so far I've tried "reverse-engineering" the problem, like saying 1.73 cube-root = 1.200, but that didn't work. I also tried removing π from 1.73, but that didn't help either. If my attempts seem stupid and pathetic, that's because I'm horrible at math, and equation-solving so pardon me for my knowledge.
Click to expand...
The "reverse-engineering" you're talking about is called algebra -- solving an equation. In order to help, we need to help you learn equation-solving skills. And for that, we need to know how far you are along that path.

If the equation you were solving was 8 = 4x, your goal would be to get x by itself, by undoing (reversing) what is done in the equation. What operation undoes multiplication by 4? Do that to both sides of the equation.

In the equation you actually want to solve, 1.73 = 4/3πr3, several things are being done to the variable r. It is being cubed, then multiplied by pi, and by 4/3. You need to undo each of those things, in the right order, in order to get r by itself. You have the idea that a cube root will undo the cube; but first you have to undo the multiplications so that there is just a cube to undo. Show us some steps, and we can help you correct them if they are wrong. But trying (and being willing to show your weakness so others can help) is the first step.
 
Dr.Peterson said:
The "reverse-engineering" you're talking about is called algebra -- solving an equation. In order to help, we need to help you learn equation-solving skills. And for that, we need to know how far you are along that path.

If the equation you were solving was 8 = 4x, your goal would be to get x by itself, by undoing (reversing) what is done in the equation. What operation undoes multiplication by 4? Do that to both sides of the equation.

In the equation you actually want to solve, 1.73 = 4/3πr3, several things are being done to the variable r. It is being cubed, then multiplied by pi, and by 4/3. You need to undo each of those things, in the right order, in order to get r by itself. You have the idea that a cube root will undo the cube; but first you have to undo the multiplications so that there is just a cube to undo. Show us some steps, and we can help you correct them if they are wrong. But trying (and being willing to show your weakness so others can help) is the first step.
Click to expand...
I did 1.73 ÷ ‭1.3333333333333333333333333333333‬, then ÷ by π, then I took the number and multiplied it by itself, the answer seemed kinda odd, I think I'm totally off with the calculations. I appreciate the help, oh and I also did the other way around (1.73 ÷ π, and so on)
 
Xentus said:
I did 1.73 ÷ ‭1.3333333333333333333333333333333‬, then ÷ by π, then I took the number and multiplied it by itself, the answer seemed kinda odd, I think I'm totally off with the calculations. I appreciate the help, oh and I also did the other way around (1.73 ÷ π, and so on)
Click to expand...
Please don't just describe what you did; show us your results at each step so wee can see where your errors are.

Your last step sounds wrong. Why would you multiply it by itself?
 
Xentus said:
So basically here's the problem :

Calculate the radius of a sphere with a volume of 1.73m3 (correct to 1 decimal place)

So far I know how to get the volume of a sphere with using either diameter, or radius, 4/3πr3 but I can't seem to figure out how to get the answer with just the volume, so far I've tried "reverse-engineering" the problem, like saying 1.73 cube-root = 1.200, but that didn't work. I also tried removing π from 1.73, but that didn't help either. If my attempts seem stupid and pathetic, that's because I'm horrible at math, and equation-solving so pardon me for my knowledge.
Click to expand...
Do you know how to calculate cube-root (in your calculator)?
 
V = (4/3)pi r^3. For now, just to see where you are, let's call (4/3)pi, K. So you have V=Kr^3. Can you solve for r^3? How about for r?
 
Jomo said:
V = (4/3)pi r^3. For now, just to see where you are, let's call (4/3)pi, K. So you have V=Kr^3. Can you solve for r^3? How about for r?
Click to expand...

r is 4.1887902047863909846168578443727 ???
 
Also guys sorry my answers are late, I have to get offline at a certain time everyday.
 
lev888 said:
Since we are given the volume and you know the formula, you get the following equation:
1.73 = 4/3πr3
Can you solve it for r?
If not, how about 8 = 4*x? Can you solve it for x?
Click to expand...

8 = 4*2
Take the 8 and divide it by 4?
 
Dr.Peterson said:
Please don't just describe what you did; show us your results at each step so wee can see where your errors are.

Your last step sounds wrong. Why would you multiply it by itself?
Click to expand...

I don't know, as I said I'm horrible at math.
 
Xentus said:
8 = 4*2
Take the 8 and divide it by 4?
Click to expand...
So, to find x we divide both sides by 4: 8/4 = (4x)/4 ===> 2 = x. Makes sense?
In general, given A = Bx, to find x we try to isolate it on one side of the equation. How do we get x if we have Bx? We divide by B. We are allowed to divide by sides by the same number. So, A/B = (Bx)/B ===> A/B = x.
If we have something like A = B*C*x we apply the same method by dividing both sides by B, then by C. Or by (B*C) - same thing.

1.73 = 4/3πr3
We can't find r right away. Let's solve for r3. Can you do it? Do you see that it looks like A=BCx? (4/3 is B, π is C)
 
Ok I hope I'm understanding correct, 1.73 ÷ ‭1.3333333333333333333333333333333‬, then ÷ π ?
Am I correct? I got ‭0.41300707732346839632025336595167‬.

Just in case I'm wrong, then here's what I attempted to do : "If we have something like A = B*C*x we apply the same method by dividing both sides by B, then by C. Or by (B*C) - same thing."
 
Xentus said:
Ok I hope I'm understanding correct, 1.73 ÷ ‭1.3333333333333333333333333333333‬, then ÷ π ?
Am I correct? I got ‭0.41300707732346839632025336595167‬.

Just in case I'm wrong, then here's what I attempted to do : "If we have something like A = B*C*x we apply the same method by dividing both sides by B, then by C. Or by (B*C) - same thing."
Click to expand...
Ok.
So, r3 = 0.41300707732346839632025336595167. Can you solve it?
This may help:

Roots calculator online (√)

Online radicals and roots calculator. Calculate the n-th root of x. Enter the root degree (n) and number (x) and press the = button.
www.rapidtables.com www.rapidtables.com
 
Xentus said:
Is the answer 0.74470767765?
Click to expand...
Yes.
Do you understand how to solve equations like this? The unknown is wrapped in several layers of operations, you need to keep taking layers off one at a time by applying the reverse of the 'outer layer' operation to both sides of the equation.
 
I think I know understand, thank you so much! How do I rate best answer?
 
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