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What shape can you
see?
SOLID GEOMETRY II
State the geometric properties of prisms, pyramids, cylinders, cones and spheres.
Draw nets for prisms, pyramids, cylinders and cones.
State and find surface areas of prisms, pyramids, cylinders, cones and spheres.
LEARNING OUTCOMES
Solid geometry is concerned with three-dimensional shapes.
Some examples of three-dimensional shapes are:
• Prisms• Pyramids• Cylinders• Cones• Spheres
DEFINITION
SOLIDS DESCRIPTION EXAMPLES
PRISM A solid with two congruent, parallel bases which are polygons.
PYRAMID A solid with a base which is a polygon and triangular sides that converge at a vertex.
CYLINDER A solid with two parallel congruent circular faces and a curved surface.
CONE A solid with a circular base and a vertex.
SPHERE A solid having all of its points the same distance from its centre.
12.1 PROPERTIES
Rectangular Prisms
Triangular Prisms
Hexagonal Prisms
Square Pyramids Rectangular Pyramid
Triangular Pyramid Hexagonal Pyramid
5 faces 8 edges 5 vertices
2 faces 2 edges 1 vertices
5 faces 9 edges 6 vertices
12.2 NETS OF GEOMETRIC SOLIDS
12.2 NETS OF GEOMETRIC SOLIDS
A net is a two-dimensional figure that can be folded into a three-dimensional solid.
EXAMPLE 1
1)
2)
3)
4)
WORKSHEET
• It is measured using squares
• Units include mm²,cm²,m²,km².
The surface area of a solid is the total area of all the faces of the solid.
12.3 SURFACE AREA
SOLIDS NETS SURFACE AREA
PYRAMID
Area of four triangular faces + Area of rectangular base
PRISM
Area of three rectangular faces + Area of two triangular faces
Example 1:
Calculate the surface area of the pyramid shown.
SOLUTION
Area of square base
10 cm
13 cm21001010 cm
Area of a triangular face
26012102
1cm
Surface area of the pyramid
2340)604(100 cm
SURFACE AREA OF CYLINDER
r r
l h
l= circumference of the base circle r2
Area of curved surface (rectangular) + Area of two circular faces.
222 rrh
Example
Find the surface area of a cylinder with a radius of 7 cm and a height of 20 cm. (Take )
7
22
SOLUTION
cmr 7 cmh 20
Surface area of the cylinder
)20)(7)(7
22(2)7)(
7
22(2 2
21188880308 cm
rhr 22 2
SURFACE AREA OF CONE
l
r r
Area of sector =
Area of circle =2r
Area of sector + Area of circle
l
rl
2rrl
Example
Calculate the surface area of a cone with a radius of 5 cm and a slant height of 8 cm. (Take )142.3
SOLUTION
cmr 5
Surface area of the cone
)5)(142.3()8)(5)(142.3( 2
223.204 cm
cml 8
2rrl
SURFACE AREA OF SPHERE
Surface area of a sphere =24 r
Where r is the radius of the sphere
Example:
Find the surface area of the sphere. (Take )
7
22
SOLUTION
Surface area of the sphere:
222 1545.37
2244 cmr
POP QUIZ
1) Find the surface area of the sphere that has
a) radius =
b) diameter =
m11
31
cm8.2
SOLUTION
a)
b) Diameter =
11
31r
22
11
14
7
2244
r 3636.20
82.2
22 )2
8.2(
7
2244 r 64.24
2) Find the value of for the solid shown in the diagram if its surface area is 1551 .
Take
h
2cm
7
22
21 cm
h cm
SOLUTION
The solid given is cylinder.2
21r ?h
155122 2 rhr
15512
21
7
222
2
21
7
222
2
h
155166693 h
85866 h13h
3) A cone has a base of diameter 14 cm. Find the slant height of the cone if its surface area 286 .
Take
2cm
7
22
SOLUTION
Diameter =14 cm 7r ?l
2862 rrl
28677
227
7
22 2
s
28615422 s
13222 l
6l
4) A sphere has a surface area of .
What is its radius?
2
7
4804 mm
Let r be the radius of the sphere.
Surface area of the sphere = 24 r
22
7
48044 mmr
7
5632
7
224 2 r
7
5632
7
88 2 r
642 r
8r
5) Calculate the value of for the following solid.
x
10 cm
x cm
Surface area = 785 cm2
SOLUTION
10r
785107
2210
7
22 22
lrrl
7857
2200
7
220l
7
3295
7
220l
97.14l
6)
12 cm
5 cm
Calculate the surface area of the cone
Solution
13 cm12 cm
5 cm
Surface area = 282.8571
7) 2.8 mm
If the diameter of the iron rod is 2.8 mm and the surface area of the rod is 2.8mm, find its length.
Solution4.1r
32.8924.17
2224.1
7
22222 22
hrrh
32.89832.128.8 h
100h
Example 1Example 1
Find the total surface area of the following solid. Take . 3.142
The solid shown below consists of a cone and a hemisphere with a common base. What is the total surface area of the solid? Take . π 3.142
“Hemi” means half.
Example 2Example 2
• Ex12.3A, Ex12.3B, Ex12.3C
HOMEWORKHOMEWORK
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