PHALOSA

Norma Trialisa

Rina Fauziah

Selviane Andini

Silvia Refina Dewi

Widyaestifa Adinugraheni

Yeshie Agustin Fadhilah

CONE

PART OF

CONE

The net of cone

2 r

s s

..……r

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

.

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)

1/3 π r2h 1/3 π r2h

1/3 π r2h

π r2 h

The Volume of Cone

V = B. h

V =

SPHERE

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.

Surface Area of Sphere

• Formula of the surface of a sphere :

A = 4 π r²

Volume of Sphere

Formula of the volume of a sphere :

V = π r³

THE EXAMPLES

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

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

c. The surface area = A of cs + ba

= 204.1 + 78.5

= 282.6 cm²

The Sphere

Given that : r =14 cm π = 22/7

Asked : Volume?

Surface Area?

SOLUTION

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

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

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

2. Find the radius of the sphere of which the surface area is 2826 cm² and π 3.14

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

“You only life once but if you do it right, once is enough “

- Maewest -

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