Find the volume of this sphere. Please help
2 answers:
Hello there!
We've already given the formula so I will not be adding it here.
We are also given that π = 3 for this problem.
r is defined as 'radius'
Radius is a point from center to one of endpoints.
Look at the image, the radius is given as 7cm.
From the information we gathered:
- π = 3
- r = 7
Substitute in the formula.
Cancel 3 out.
Evaluate 7^3
Multiply
Therefore, the volume is 1372.
Let me know if you have any questions!
Topic: Surface Area and Volume - Sphere's Volume
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We have:
Thus:
Adding
gives:
Factoring gives:
Thus, we have:
or
.
Note that because
, there will be no solutions 
of the form 
for positive integer 
and solution 
. So we find the basic values of 
giving 
.
For with positive , 
(this can be seen easily from the unit circle. But 
, a contradiction. So we examine the case in which .
In this case,
. So this is the only solution to this equation.
Substituting this back in, we have
, as desired. So this is a valid solution.
Thus,.
Thus:
Adding
Factoring gives:
Thus, we have:
or
Note that because
For
In this case,
Substituting this back in, we have
Thus,