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.Com
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) (Show Source): 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.
RELATED QUESTIONS
what is the lateral surface area of a right hexagonal prism whose base is a regular... (answered by Alan3354)
A rectangular prism has a base area of 400 square inches. The volume of the prism is 2 ,... (answered by KMST)
A wooden jewelry box has the shape of a prism with a regular
hexagonal base of... (answered by solver91311)
a right regular hexagonal prism is inscribed in a right circular cylinder whose height is (answered by ikleyn)
`a right regular hexagonal prism is inscribed in a right circular cylinder whose height... (answered by greenestamps)
The volume of a regular hexagonal prism of length 10cm, where the sides of the hexagon is (answered by greenestamps)
Thank you in advance for help:)
A jewelry box has the shape of a prism with a regular... (answered by Theo)
A regular hexagonal pyramid has 24 cm sloping edge. If the length of side of the hexagon... (answered by solver91311)
each of the bases of a right prism is a regular hexagon with one side which measures 6... (answered by solver91311)