First of all the volume of a sphere is 4/3 pi r^3, not 3/4 pi r^3.
You have to determine how much of the volume of the egg was submerged, knowing what fraction of the area was submerged. They are not the same fractions. The solution requires calculus. Let y be the distance of the center of the sphere below the water line. The area above the water line is 28% of 4 pi r^2 or 1.12 pi r^2
Derive a formula for the angle theta between the vertical and the water line, which is cos^-1 (y/r), using calculus, and solve for theta.
I think you will find that the area above water is 2 pi r^2 cos theta. Since that is 1.12 pi r^2, the angle theta is cos^-1 0.56 = 55.94 degrees.
Once you know theta, derive another equation for the fraction of the sphere below the water line, also in terms of theta. Then you can solve for the total sphere volume.
You came across an egg that was a perfect sphere. You placed it in a tub of water and found that it displaced exactly 280,000 cubic centimetres. However, it was floating on the water, and only 72% of the surface area of the egg was below the water line.
What was the total volume of the egg, in cubic centimetres?
Isn't the volume of a sphere 3/4 pi r^3?
How would I go about solving this problem?
1 answer