Describes the geometrical formulas ball and coneMembers :1. Andre djisa alhesi samosir2. Dicky rachmat fauzi3. Erlangga putra ramadhan4. Haekal roja5. Jihan fachry widyatmoko6. Yogas adi pratama
Cone 1. Geometrical cone is bounded by a circular base side and a curved side . T = elements of cone = 1. A cone has 2 planes . Namely the base and the right planes 2. A cone has an edge , that is the base edge which is in the form of circle 3. The line segment joining point t and T1 is called the height of the cone A T1 B 4. TA and TB are called slant heights.
= cone net =1. To know the net of a cone T suppose the cone in figure 2 is cut along segment TA and its base circumference , the cuts s will produce the figure on the figure 1. 12. The figure 1 shows the net of a 2 cone , the cone consist of a A B circle and a curved surface in the form of a circle sector . T1
= surface area of a cone =We need to know that, the surface of L = surface areathe cone consists of two fields, namely Ba = base areathe curved area (blanket) and a Cs = curved areacircular base field. Sa = surface areaFormula of the surface area of a cone :L = area of curved surface + circle areaL = ∏ r s + ∏ r2L=∏r (s+r)Example :Known : d : 10 , t : 12 , Cs : 204,1 , Ba : 78,5Find : SaAnswer :L = Cs + Ba => 204,1 + 78,5 = 282,6 cm2
= volume of cone =Formula of volume of cone : ∏ x r x r x h : 3 (∏ x r2 x h x 1/3) Example : Known : d : 14 , t : 18 , ∏ : 22/7 Find : volume Answer : Volume : ∏ x r2 x h x 1/3 => 22/7 x 7 x7 x 18 x 1/3 = 924
=the ratio of cone because of the change= in radiusFigure 1 illusrates a cone of base radius r1 andheight t . 1If the base radius r1 is extended twice longerwhile the hight is constant , we have a cone infigure 2 of base radius r2 = 2 r1 and height tThen : v1 = 1/3 ∏ r21 t v2 1/3 ∏ r2 2 t 2 v1 = 1/3 ∏ r21 t v1 = r21 v2 1/3 ∏ (2r 2 ) t v2 4 r2 1 v1 = 1 v2 = 4 v 1 v2 4
Example :Known : r : 6 , ∏ : 22/7Find : the volume of the cone if the becomes 2x the originalAnswer :V = 1/3 ∏ r2 t 1/3 x 22/7 x 6 x 6 x 21 792r1= 2r then v1 = 22 v 4 x 792 = 3.168
SphereSphere represent a curved surface= elements of sphere =1. Point O is the centre of the sphere2. DO , AO ,BO , CO etc called radius of sphere3 .DC , AB etc is called diameter of sphere4. A sphere only has one curved surface5. A sphere doesn’t have a vertex nor an edge C A O B D
= sphere net =We can’t make a net from a sphere
= the surface area of a sphere = Sa of a sphere= 2 x the area hemisphere 2 x ( 2 x ∏ r2 ) = 4∏r2 example : Known : r : 10,5 , ∏ : 22/7 Find : Sa Answer : L = 4∏r2 4 x 22/7 x 10,5 x 10,5 = 1,386
= volume of sphere =v = 4 x the cone volume 4 x 1/3 ∏ r2 t 4/3 ∏ r2 tSince the height of the cone = the ball radius , or t = rThe ball volume : 4/3 ∏ r2 t = 4/3 ∏ r3Example :Known : d : 12 , ∏ : 3,14Answer :V : 4/3 x ∏ x r3 4/3 x 3,14 x 6 x 6 x 6 = 904,32 cm cm3
the ratio of the sphere volume because of the change in radius If the radius of a sphere is extented n times the original , then the volume of the sphere enlarges n3 times the original volume , in other words v1 : v1 = 1 : n3Example :Known : v : 113,04 cm3find : 3/2 times the original lengthAnswer : r1 = 3/2 r => v1 = (3/2)3 v = 27/8 x 113,04 = 381,51
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