Download - cone and sphere
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PHALOSA
Norma Trialisa
Rina Fauziah
Selviane Andini
Silvia Refina Dewi
Widyaestifa Adinugraheni
Yeshie Agustin Fadhilah
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CONE
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PART OF
CONE
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The net of cone
2 r
s s
..……r
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The surface Area of Cone
How To find the surface Area of The cone?To find the surface area of the cone, we need to calculate all the areas of the laterals.So, we need to find:the area of curved area and circle area
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.
Surface Area of Cone
L = area of sectorA B
--------r
Base
Area of sector = Circumference of base Area of big circle = Circumference of big circle
Area of sector =
=
=
=
The surface area of cone (SA) equals the sum of the area of the sector ( or lateral face) (LA)and the area of the base (B)
Surface Area of Cone SA = LA + B = π r s + π r² = π r (s + r)
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1/3 π r2h 1/3 π r2h
1/3 π r2h
π r2 h
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The Volume of Cone
V = B. h
V =
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SPHERE
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Center of sphere
The Radius of sphere
A
B
----------- C
Point O is the center of the sphere. Point AO is the radii of the sphere. AC is one of the diameter in the sphere. Sphere only has one curved surface. Sphere doesn’t have a vertex nor an edge.
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Surface Area of Sphere
• Formula of the surface of a sphere :
A = 4 π r²
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Volume of Sphere
Formula of the volume of a sphere :
V = π r³
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THE EXAMPLES
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The Cone
• A cone has a base plane diameter of 10 cm and height of 12 cm. For π = 3.14 :
a. The curved surface area
b. The base area
c. The surface area
SOLUTION
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Given that : d = 10 cmh = 12 cmπ = 3.14
• s = √h² + r² = √12² + 5² = √144 + 25 = √ 169 ↔ s = 13 cm
a. The curved surface area = π r s = 3.14 x 5 x 13 = 204.1 cm²
b. The base area = π r² = 3.14 x 5 x 5 = 78.5 cm²
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c. The surface area = A of cs + ba
= 204.1 + 78.5
= 282.6 cm²
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The Sphere
Given that : r =14 cm π = 22/7
Asked : Volume?
Surface Area?
SOLUTION
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Volume = 4/3 x π x r³
= 4/3 x 22/7 x 14³
= 4/3 x 22/7 x 2744
= 4/3 x 22 x 392
= 11498.7 cm³
Surface Area = 4 . π . r² = 4 . 22/7 . 14² = 4 . 22 . 28 = 88 . 28 = 2464 cm²
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EXERCISE
1. A cone has a base radius of 7cm. If the area of its curved surface is 550cm² and π = , find:
a. The slant height
b. The surface area
c. The height of cone
22
7
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Solution a. Cs = π r l
550 = x 7 x l
550 = 22s
s = l = 25cm
b. SA = π r (l+r)
= x 7 x (25+7)
= 22 x 32 704 cm²
c. h = √l² - r²
= √25² - 7²
= √576 h = 24cm
227
55022
227
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2. Find the radius of the sphere of which the surface area is 2826 cm² and π 3.14
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Solution
Given that : Sa = 2826 cm²
π = 3.14
Asked : r = ?
Answer : Sa = 4 π r²
2826 = 4 x 3.14 x r²
r = √2826
r = √225
r = 15 cm
4 x 3.14
900
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“You only life once but if you do it right, once is enough “
- Maewest -
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THANK YOU