The document provides information about geometric shapes including cones, spheres, and their measurements. It defines formulas for calculating the surface area and volume of cones and spheres. It then works through examples of applying the formulas to find specific measurements of given cones and spheres. Finally, it provides exercises for the reader to practice calculating surface areas, volumes, radii and other values of cones and spheres using the defined formulas.

1. PHALOSA
Norma Trialisa
Rina Fauziah
Selviane Andini
Silvia Refina Dewi
Widyaestifa Adinugraheni
Yeshie Agustin Fadhilah

2. CONE

4. The net of cone
s s
2 r
..……
r

5. 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

6. Surface Area of Cone
Area of sector = Circumference of base
Area of big circle = Circumference of big
. circle
L = area of sector Area of sector =
A B
r =
-----
---
=
Base =
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)

7. π r2 h
1/3 π r2h 1/3 π r2h
1/3 π r2h

8. The Volume of Cone
V= B. h
V=

9. SPHERE

10. Center of sphere
 Point O is the center of the sphere.
A ----------- C  Point AO is the radii of the sphere.
 AC is one of the diameter in the
B sphere.
 Sphere only has one curved surface.
 Sphere doesn’t have a vertex nor an
edge.
The Radius of
sphere

11. Surface Area of Sphere
• Formula of the surface of a sphere :
A = 4 π r²

12. Volume of Sphere
Formula of the volume of a sphere :
V = π r³

13. THE EXAMPLES

14. 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

15. Given that :
d = 10 cm
h = 12 cm
π = 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

16. c. The surface area = A of cs + ba
= 204.1 + 78.5
= 282.6 cm²

17. The Sphere
Given that : r =14 cm
π = 22/7
Asked : Volume?
Surface Area?
SOLUTION

18.  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

19. EXERCISE
1. A cone has a base radius of 7cm. If the area of
its curved surface is 550cm² and π = 22 , find:
7
a. The slant height
b. The surface area
c. The height of cone

20. Solution
a. Cs =πrl
22
550 = 7 x7xl
550 = 22s
550
s = 22 l = 25cm
b. SA = π r (l+r)
22
= 7 x 7 x (25+7)
= 22 x 32 704 cm²
c. h = √l² - r²
= √25² - 7²
= √576 h = 24cm

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

22. Solution
Given that : Sa = 2826 cm²
π = 3.14
Asked : r = ?
Answer : Sa = 4 π r²
2826 = 4 x 3.14 x r²
900
r = √2826
4 x 3.14
r = √225
r = 15 cm

23. “You only life once but if you do it
right, once is enough “
- Maewest -

24. THANK YOU