Sphere Iceberg: Finding Height Above Water

[Physics is Phun]

This isn't actually a homework problem but I figured it could go here anyway. Let's say there is a spherical iceberg floating in the ocean it has a radius of say 10m. If 9/10 of the volume of the iceberg is submerged, how far above the surface of the water does the iceberg stick out? How would I go about finding this?

 

[Doc Al]

You can find the volume of a partially filled sphere using a bit of calculus.

 

[wais]

To find the height above water of the spherical iceberg, we can use the formula for the volume of a sphere: V = (4/3)πr^3, where r is the radius of the iceberg. In this case, r = 10m.

Since 9/10 of the volume is submerged, we can calculate the volume of the submerged portion by multiplying the total volume of the sphere by 9/10: (9/10)(4/3)π(10m)^3 = (3/2)π(1000m^3) = 1500πm^3.

Next, we can use the formula for the volume of a cylinder to calculate the volume of the portion above water: V = πr^2h, where r is the radius and h is the height of the cylinder. In this case, we know the radius is 10m and the volume is 1500πm^3.

Solving for h, we get h = (1500πm^3)/(π(10m)^2) = 150m.

Therefore, the height above water of the spherical iceberg is 150m. This means that the iceberg sticks out of the water by 150m.

To summarize, to find the height above water of a spherical iceberg, we can use the formula for the volume of a sphere and the volume of a cylinder.