Answer:
Ves = 169.56 cm³
Explanation:
Let call Vc volume of cylinder
If the cylinder has to contain three spheres of radius 3 cm the height of the
cylinder is 3 * 2 * 3 = 18 cm ( we have three diameters )
The radius of the base of the cylinder is 3 cm
And Vc = π*r²*h ⇒ Vc = (3,14) * 9 * 18 ⇒ Vc = 508.68 cm³
On the other hand we have Vs (volume of one sphere)
Vs = 4/3 * π * r³ ⇒ Vs = 4/3 * 3,14 * (3)³ ⇒ Vs = 113,04 cm³
as we have 3 spheres the total volume is 3 * 113.04
Vts = (total volume of spheres) = 339,12 cm³
The empty space withing the cylinder is the difference between Vc and Vts
Ves ( volume of empty space ) = Vc - Vts = 508.68 - 339,12
Ves = 169.56 cm³