Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere which is shown below.
Here, we are given that our sphere has a radius of 4 units.
So plugging into the formula, we have .
Start by simplifying the exponent.
(4 units)³ is equal to (4 units) (4 units) (4 units) or 64 units³.
So we have .
Next, we multiply (4/3)(64) which can
be thought of as (4/3)(64/1)
So multiplying across the numerators and across the denominators,
we have .
So with this, we will be using proportions. To solve for x, our proportion will be
Firstly, cross-multiply:
Next, subtract 36 on both sides:
Next, replace -9x with 3x-12x
Next, factor x^2+3x and -12x-36 separately: . After, rewrite it as
Next, solve for x separately in the two parentheses:
Since we can't have a negative length, x = 12.
To solve for y, our proportion will be
Firstly, cross-multiply:
Next, just square root each side, and your answer will be (rounded to hundredths)
In short, x = 12 and y = 10.39.