The volume of a sphere of radius r is V=4/3πr^3.Solve for r.
so, solve for r...
V = 4π/3 r^3
r^3 = 3V/(4π)
...
To solve for the radius (r) in the volume formula of a sphere (V = 4/3πr^3), we need to isolate the variable r. Let's go step by step.
1. Start with the given volume formula:
V = 4/3πr^3
2. Multiply both sides of the equation by 3/4 to cancel out the fraction:
(3/4)V = (3/4)(4/3πr^3)
(3/4)V = πr^3
3. Divide both sides of the equation by π:
(3/4)V/π = (πr^3)/π
(3/4)V/π = r^3
4. Take the cube root of both sides of the equation to solve for r:
∛((3/4)V/π) = ∛(r^3)
∛((3/4)V/π) = r
Thus, the expression ∛((3/4)V/π) represents the radius (r) of a sphere in terms of its volume (V). By substituting the value of V into this expression, you can calculate the radius.
To solve for the radius (r) of a sphere using the volume formula V = (4/3)πr^3, we need to isolate r on one side of the equation.
Step 1: Start with the given equation: V = (4/3)πr^3
Step 2: Divide both sides of the equation by (4/3)π to isolate r^3.
V / ((4/3)π) = r^3.
Step 3: Simplify the right side of the equation.
(3V) / (4π) = r^3.
Step 4: Take the cube root of both sides of the equation to solve for r.
∛((3V) / (4π)) = r.
Therefore, the formula to solve for the radius (r) of a sphere with a given volume (V) is r = ∛((3V) / (4π)).