A dome or cap is created by slicing off the top of a sphere halfway along its radius. What is the volume of the dome as a percentage of the volume of the sphere? Please note that it is the radius that is bisected, not the diameter, so the dome is smaller than a hemisphere.
HINT: Use the volume of revolution by applying calculus to the equation of a unit circle: x^2+y^2=1. By integrating between the limits 0.5 to 1 and using the summation of the volumes of thin discs you can work out the volume of a dome and divide this by the volume of a unit sphere.
