Question

If a spherical metal bob of radius 3cm is fully immersed in a cylinder containing water and the water level rises by 1cm, what is the radius of the cylinder?

Answer 1

When we drop the sphere into the cylinder of water, it sinks to the bottom.
How much water is displaced by the sphere we dropped in?
The volume of a sphere is given by
V_sphere=4/3 πr_sphere^3
Now that we know the amount of water that 'moved', and we know the container holding that water is a right circular cylinder, all we need to know is the formula for the volume of such a cylinder.
V_cylinder=hπr_cylinder^2

Now we can equate those two volumes and solve for r_cylinder
4/3 πr_sphere^3=hπr_cylinder^2
r_cylinder=√((4r_sphere^3)/3h)=√((4×(3)^3)/(3×1))=√(4×3^2 )=2×3=6 cm

Answer: 6 cm.