A right triangle with sides 3cm and 4am is revolved around its hypotenuse. Find the volume of the double cone thus generated.
2006-07-13 03:49:20 · 7 answers · asked by g 2 in Science & Mathematics ➔ Mathematics
in mathematics, the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex). The path, to be definite, is directed by some closed plane curve (the directrix), along which the line always glides. In a right circular cone, the directrix is a circle, and the cone is a surface of revolution. The axis of this cone is a line through the vertex and the centre of the circle, the line being perpendicular to the plane of the circle. In an oblique circular cone, the angle that the axis makes with the circle is other than 90°. The directrix of a cone need not be a circle; and if the cone is right, planes parallel to the plane of the directrix produce intersections with the cone that take the shape, but not the size, of the directrix. For such a plane, if the directrix is an ellipse, the intersection is an ellipse.
The generatrix of a cone is assumed to be infinite in length, extending in both directions from the vertex. The cone so generated, therefore, has two parts, called nappes or sheets, that extend infinitely. A finite cone has a finite, but not necessarily fixed, base, the surface enclosed by the directrix, and a finite, but not necessarily fixed, length of generatrix, called an element
solve it yourself
2006-07-13 03:59:30 · answer #1 · answered by Anonymous · 0⤊ 0⤋
2+2=5
2006-07-13 11:06:04 · answer #2 · answered by MDR 2 · 0⤊ 0⤋
first you should take a cross section of the double cone. the cross section will be a kite. Since we know the area of the kite is 12 (the area of each kite was 6 and there was 2 of them) and one of the diaganols is 5 (the hypotenuse) the other diagnol must make the product of the diaganols 24 so the kite's area is 12. This works out so the other diaganol is 4.8. Using the pythagereom thereom, we know the heights of the triangles are 3.2 and 1.8. 3.2 * 4.8 / 3 = 15.36 which is the area of the larger cone. 1.8 * 4.8 / 3 = 2.88. If u add them together u get 18.24 as the final answer of the total volume.
2006-07-13 11:05:34 · answer #3 · answered by Russel 1 · 0⤊ 0⤋
If you rotate around hypotenuse you wont get a perfect cone. Bottom will not be flat.
Volume of cone is.
one third of Bottom area times height
bottom area is pie x d square / 4 ( circle)
do the math
if b is the length of the bottom then the vol = 1/3 pie b square *height
2006-07-13 10:57:31 · answer #4 · answered by Dr M 5 · 0⤊ 0⤋
Volume of a cone =(3.1416 x 9/4 x 4)/3
= 9.4248 cu. cm
since its a double multiply it by 2, thus:
9.4248 x 2 = 18.8496 cu. cm
2006-07-13 11:00:19 · answer #5 · answered by baeyongmok 2 · 0⤊ 0⤋
this is a basic geometry question.. you should do your own homework questions..
2006-07-13 10:55:35 · answer #6 · answered by valiantw2001 2 · 0⤊ 0⤋
lol you joking right
2006-07-13 10:51:54 · answer #7 · answered by worldstiti 7 · 0⤊ 0⤋