Question #71314

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?

Expert's answer

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.

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.

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