A right circular cone with altitude h and base r is equal to (1/3)*pi*r2*h. This is one third of the volume of a right cylinder with the same dimensions, and can be written as (1/3)*A*h where A is the area of the base circle.
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This question has already been answered along with the workings. The answer is: 9.947183943 inches
The simple is to calculate the volume of the cone and subtract from the result the volume of the cone whose altitude is 1/2 the altitude of the original cone. This is easier said than done. The volume of a cone with circular base is (1/3)πr2s where r is the radius of the base and s is the altitude. The radius of the base of the empty part of the cone and hence its area can be found by using the pythagorean theorem
The volume of a right circular cylinder is found by using this formula: V=pi/4*r2*height Note: In this case, altitude and height are the same thing. Fill in the measurements you are given and solve. 500 = (3.14)(4)2(height) 500 = (3.14)(16)(height) 500 = (50.24)(height) height = approximately 9.95 inches
Spheres are spherical, with no base, and have no flat surfaces. Cones have a flat, circular base, with a circular altitude protruding from the edges of the circle. The altitude's diameter slowly diminishes until all edges reach eachother.
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