CONEa.) Definition of Cone A cone is a dimensional geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex.h : heights : slant heightr : radius
B. ELEMENTS OF A CONEa) A cone has 2 planes, namely the base and the right planes. The base is circular plane of radius r or BO, while the right plane is a curved which is also called curved surface.
b) A cone has an edge, that is the base edge which is in the form of a circle. Circle
c) The line segment joining point O to A is called the height of the cone. Usually it is notated by h or t.d) The line segment of the curved surface joining vertex A and the points of the circle are called slant heights. A slant height is usually notated by s or l.
C. PaRt of Cone The circle at the bottom of a cone defines the shape of the cone, so all of the parts of a circle are important parts of a cone. For example, the radius is an integral part of finding the volume of a cone.
D. THE SURFACE AREA OF A CONE Sector TAA’ is in the circle of radius TA or of radius s/l, so that :The area of sector TAA’ = the length of arc AA’The circle area the circle circumferenceThe area of sector TAA’ = 2πr πs 2 2πsThe area of sector TAA’ = 2πr × πs 2 2πsThe area of sector TAA’ = πrsThe area of the curved surface = the area of sector TAA’ = πrs
The surface area of a cone is equal to thearea of its net, or it can be expressed by thefollowing formula.L = area of curved surface + circle area = π rs + π r2 = π r (s + r)
The formula of the surface area of a cone is: L = π r (s + r) Where L = the surface area of the cone π = 22 or π = 3,14 7 r = circle radius (base plane of the cone) s = slant height of the cone
E.) EXAMPLE1) A cone has a base radius of 7 cm. If the area of its curved surface is 550 cm2 and π = 22 find : 7 a. The slant height b. The surface area of the cone c. The height of the cone
Solution: Given that r = 7 cm, area of curved surface = 550 cm2, and π = 22 7a. The area of curved surfaces = π rs 550 = 22 × 7 × s 7 550 = 22s s = 550 22 s = 25 cm
b. L = π r (s + r) = 22 × 7 × (25 + 7) 7 = 22 × 32 = 704 cm2c. ⇔ t = 24 cm.
F.) EXERCISE1) A cone has a base radius of 14 cm. If the area of its curved surface is 957 cm2 and π = 22 find 7 a. The slant height b. The surface area of the cone
Solution: Given that r = 7 cm, area of curved surface = 957 cm2, and π = 22 7a. The area of curved surfaces = πrs 957 = 22 × 7 × s 7 957 = 22s s = 957 22 s = 29 cm
b. L = π r (s + r) = 22 × 7 × (29 + 7) 7 = 22 × 36 = 792 cm2
QUOTES If A is a success, then the formula is A = X + Y + Z, where X is the working, Y is play, and Z is keep your mouth to keep it closed.Jika A adalah ‘sukses’, maka rumusnya adalah ‘A=X+Y+Z’, dimana X adalah ‘kerja’, Y adalah ‘bermain’, dan Z adalah jaga mulut anda agar tetap tertutup.Pendidikan adalah mata uang yang berlaku di seluruh dunia