You can
put this solution on YOUR website!The volume of a right prism is given by the area of the base times the height (altitude). Since you know the volume, divide it by the area of the base. The area of a regular hexagon in terms of the length of a side is:
where t is the length of the side.
The volume of a right circular cone is
where r is the radius of the base and h is the height. The volume of a sphere of radius r is
. The volume of a cone can be re-written as:
. So the ratio of the volume of a sphere to a cone with a base diameter equal to the diameter of the sphere would be
The formula for the volume of a sphere is in the paragraph above. Use it.
Construct the perpendicular bisector of the chord. It will intersect the circle center. This forms a right triangle with half the cord as one side and the radius intersecting one endpoint of the cord as the hypotenuse. The angle between the constructed line and the radius through the cord endpoint is
. (10 divided by 12 comes from half the chord divided by the radius) Twice this angle is the central angle defined by the endpoints of the chord. The area of a circle segment, in terms of the radius of the circle and the central angle is:
if you calculate
in radians, or
if you calculate
in degrees. Where
is the central angle and r is the radius.
