How do you find an explicit formula?
1 answer:
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By definition, the volume of a sphere is:
Where,
r: sphere radio
Substituting values we have:
Rounding the result to the nearest tenth:
Answer:
the sphere's volume is:
Where,
r: sphere radio
Substituting values we have:
the sphere's volume is:
Lets say that the two unknown integers are 
and 
.
We know the following things about and :
And, we want to find
.
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for:
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of and , which are 12 and 14, and directly compute their product; however, the approach described is more elegant.
We know the following things about
And, we want to find
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of