Final answer:
To calculate the value of r, we need to find the volume of the two spheres and subtract it from the volume of the cylinder. Setting up an equation and solving for r, we find that r = 5/2.
Step-by-step explanation:
To calculate the value of r, we need to find the volume of the two spheres and subtract it from the volume of the cylinder.
The volume of a sphere is given by the formula V = (4/3)πr³.
Since there are two spheres, the total volume of the spheres is (8/3)πr³.
The volume of the cylinder can be calculated using the formula V = πr²h, where h is the height of the cylinder. Substituting the given values, we have V = πr²(4r) = 4πr³.
Now we can set up an equation to solve for r:
4πr³ - (8/3)πr³ = 125/6π
Simplifying the equation, we get:
(12/3 - 8/3)πr³ = 125/6π
(4/3)πr³ = 125/6π
Dividing both sides of the equation by (4/3)π, we get:
r³ = (125/6π) / (4/3)π
r³ = (125/6) / (4/3)
r³ = 125/8
Taking the cube root of both sides of the equation, we get:
r = ∛(125/8)
r = 5/2