1. CYLINDER, CONE AND SPHERE
Solid Geometry
CYLINDER, CONE AND SPHERE
CONE

2. SOLIDS Standards 8, 10, 11 PYRAMID PRISM SPHERE CYLINDER CONE
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

3. Cylinder Has three faces, they are two bases and a lateral face/curved
surface
Has two edges
radius
Height

5. SURFACE AREA OF CYLINDERS
base r 2
2 r h h
2 r h r
base r r 2
Lateral Area:
2 r
L = h
Total Surface Area = Lateral Area + 2(Base Area) T=
2 r h + 2 r
h= height
r= radius

6. VOLUME OF CYLINDERS r 2 B= h r
V = Bh
V = r 2 h
RIGHT CYLINDER

7. Total Surface Area = Lateral Area + 2(Base Area)
Find the lateral area, the surface area and volume of a right cylinder with a radius of 20 in and a height of 10 in.
Total Surface Area = Lateral Area + 2(Base Area) T=
2 r h + 2 r
T = 2 ( )( ) ( ) 2
10 in
20 in
10 in
20 in
20 in
T= in + 2(400 in ) 2
T = in 2
Lateral Area:
T = 1200 in 2
2 r
L = h
L = 2 ( )( )
20 in
10 in
Volume:
V = r 2 h
L=400 in 2
V =
( ) 2
20 in
10 in
V= (400 in )(10 in) 2
V= in 3

8. cone Has two faces Note: * r = radius * h = height * s = slant height

9. How to calculate the curved surface area ?
Cut here

10. How to calculate total surface area of a cone?+ r
Total surface area =πr2 + πr l

11. Surface Area of a Cone
A cone has a circular base and a vertex that is not in the same plane as a base.
In a right cone, the height meets the base at its center.
The height of a cone is the perpendicular distance between the vertex and the base.
The slant height of a cone is the distance between the vertex and a point on the base edge.
The vertex is directly above the center of the circle.
Height
Lateral Surface
Slant Height r
Base r

12. SURFACE AREA OF A RIGHT CIRCULAR CONE L= area of sector 2 r 2 r C=
perimeter of cone’s base
Area of Circle 2 l h r l r 2 r C= 2 r B= 2 C= l
area of sector
perimeter of cone’s base =
area of circle
perimeter of circle
TOTAL SURFACE AREA:
area of sector 2 r =
T = area of sector + area of cone’s base 2 l 2 l
h= height
T = L + B 2 l r 2 l =
area of sector
r = radius T= 2 r l +
l = slant height
area of sector l r = L=
Lateral Area

13. VOLUME OF A RIGHT CIRCULAR CONE
Standards 8, 10, 11
VOLUME OF A RIGHT CIRCULAR CONE h r
V = Bh 1 3
V = 2 r 1 3 h 2 r B=
h= height
r = radius

14. Examples 1 a) If h = 12cm, r= 5 cm, what is the volume? Answer:
Volume = πr2h 1 3 1 3
= π (52) ( 12)
= 314 cm3

15. b) what is the total surface area?
= π52
Based Area
= 25πcm2
Slant height
= 
= 13 cm
Curved surface area
= π(5) ( 13)
= 65π cm2
Total surface area
= based area + curved surface area
= 25π+65π= 90π
= 282.6cm2 (corr.to 1 dec.place)

16. Calculating the base area: 10 cm = r B=
Find the lateral area, the surface area and volume of a right cone with a height of 12 cm and a radius of 10 cm. Round your answers to the nearest tenth.
Lateral Area: h r l l r L=
L= (12 cm ) (13 cm ) = cm 2
=12 cm
Calculating the base area:
10 cm = 2 r B=
B= ( 5 ) 13
B= cm
T = L + B
T = cm
B = (25) (13)(3.14)
Calculating the volume: 2 r
V = 1 3 h
V = ( 5 ) (12)
V = 314 cm 2 r B=
we need to find the slant height, using the Pythagorean Theorem: l = 2
V = 1 3
( 25 ) ( 12 )
Calculating surface area:
l = 2
l = 2
T = cm cm 2
l = 13

17. Sphere has no flat surface just has a face
Notice the shadowing to show that it is not a circle

20. r r

21. From the experiment that you have done:
Determine how many circles could be covered by that rope
The area of a hemispherical = the area of 2 circles
The area of 2 hemispherical = the area of 4 circles
The area of a sphere = the area of 4 circles
A = 4 the area of a circle
A = 4 πr2

22. Volume of Cylinder
Volume of the sphere

23. Solve the following problem:
A solid spherical object has a diameter of 4.2 cm.
Find out the surface area of the object
2. What is the radius of the sphere, if the area of
the sphere is 78 cm2
3. A solid spherical object has a radius of 20 cm.
Find out the surface area of the object

24. A solid spherical object has a diameter of 4.2 cm.
Find out the surface area of the object .
Solution
The diameter is 4.2 cm r = 2.1 cm
The formula of the surface area is
A = 4 πr2
A = 4 πr2
A = (2.1)2
A = cm2
Therefore, the surface area of that object is cm2

25. PROBLEM SOLVING

26. The silo shown below has been built from metal.
PROBLEM SOLVING
The silo shown below has been built from metal.
The top part of the silo is a cylinder of diameter 4 m and height 8 m. The bottom part of the silo is a cone of slant height 3 m. The silo has a circular opening of radius 30 cm on the top.
What area of metal (to the nearest m2) was required to build the silo?
b. If it costs Rp25, per m2 to cover the surface with an anti-rust material, how much will it cost to cover the silo completely?

27. solution Understanding the problem
What is the unknown?
The area of the metal and cost to cover the surface
b. What are the data?
A cylinder with a diameter 4 m and height 8 m.
The bottom part of the silo is a cone with a slant height 3 m.
The silo has a circular opening with a radius 30 cm on the top.
It costs Rp25, per m2 to cover the surface with an anti-rust material

28. 2. Developing a plan and strategy a
2. Developing a plan and strategy a. Find the surface area of the top face. b. Find the area of the curved part of cylinder. c. Find the area of the curved section of a cone. d. Find the area of the silo by adding the area of the top face the curved part of cylinder and the curved section of a cone. e. The total cost can be obtained by multiplying total area by the cost per m2.

29. 3. Carrying out the plan a. The area of the top face = the area of a large circle – the area of a small circle. = 3.14(22) (0.32 = 3.14( = m2 b. The area of the curved part of cylinder = 2(3.14)(2)(8) = m2 c. The area of the curved section of a cone = rs = (2)(3) = m2 d. The area of the silo = m m m2 = m2 e. Total cost = 132(Rp 25,000.00) = Rp3,300,0