SOLUTION: 1. A hexagonal right prism has a volume of 500 cubic inches. If the base is a regular hexagon with a side 4 inches. What is the altitude of the prism? Round off your answer to two

Algebra ->  Bodies-in-space -> SOLUTION: 1. A hexagonal right prism has a volume of 500 cubic inches. If the base is a regular hexagon with a side 4 inches. What is the altitude of the prism? Round off your answer to two       Log On


   

Question 132596: 1. A hexagonal right prism has a volume of 500 cubic inches. If the base is a regular hexagon with a side 4 inches. What is the altitude of the prism? Round off your answer to two decimal places.
2. What is the ratio of the volume of a sphere and a cone with the base diameter of the sphere?
3.How many cubic inches of material are needed for a solid rubber ball with a diameter of 3 inches? Round off your answer to two decimal places.
4.What is the approximate area of a segment of circle with a radius 12 meters if the length of the chord is 20 meters?
Answer by solver91311(24713) About Me  (Show Source):
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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: A=%28%283%2Asqrt%283%29%29%2F2%29t%5E2 where t is the length of the side.

The volume of a right circular cone is V=%281%2F3%29pi%2Ar%5E2h where r is the radius of the base and h is the height. The volume of a sphere of radius r is %284%2F3%29pi%2Ar%5E3. The volume of a cone can be re-written as: V=%281%2F3%29pi%2Ar%5E3%28h%2Fr%29. 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 %28%284%2F3%29pi%2Ar%5E3%29%2F%28%281%2F3%29pi%2Ar%5E3%28h%2Fr%29%29=4r%2Fh

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 arcsin%2810%2F12%29. (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:

%281%2F2%29r%5E2%28alpha-sin%28alpha%29%29 if you calculate arcsin%2810%2F12%29 in radians, or %281%2F2%29r%5E2%28%28pi%2F180%29alpha-sin%28alpha%29%29 if you calculate arcsin%2810%2F12%29 in degrees. Where alpha is the central angle and r is the radius.