Solid Geometry II - Slide

5/22/2018 Solid Geometry II - Slide

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What shape can

you see?


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SOLIDGEOMETRY II


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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


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Solid geometry is concerned with

three-dimensional shapes.

Some examples of three-dimensional

shapes are:

Prisms

Pyramids

Cylinders

Cones

Spheres

DEFINITION


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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 avertex.

CYLINDER A solid with two parallel congruent

circular faces and a curved surface.

CONE A solid with a circular base and avertex.

SPHERE A solid having all of its points the same

distance from its centre.

12.1 PROPERTIES


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Rectangular Prisms

Triangular Prisms

Hexagonal Prisms


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Square Pyramids Rectangular Pyramid

Triangular Pyramid Hexagonal Pyramid


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5 faces8 edges

5 vertices

2 faces2 edges

1 vertices

5 faces9 edges

6 vertices


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12.2 NETS OF GEOMETRIC

SOLIDS

A net is a two-dimensional

figure that can be folded

into a three-dimensional

solid.


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EXAMPLE 1

1)

2)


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3)

4)


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WORKSHEET


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It is measured using squares

Units include mm,cm,m,km.

The surface area of a solid is the

total area of all the faces of the

solid.

12.3 SURFACE AREA


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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


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Example 1:

Calculate the surface area of the pyramid shown.


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SOLUTION

Area of square base

10 cm

13 cm21001010 cm

Area of a triangular face

2601210

21 cm

Surface area of the pyramid

2340)604(100 cm


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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


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Example

Find the surface area of a cylinder

with a radius of 7 cm and a height of

20 cm. (Take )722


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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


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SURFACE AREA OF CONE

l

r r

Area of sector =

Area of circle =2

r

Area of sector + Area of circle

l

rl

2rrl


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Example

Calculate the surface area of a cone

with a radius of 5 cm and a slant

height of 8 cm. (Take )142.3


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SOLUTION

cmr 5

Surface area of the cone

)5)(142.3()8)(5)(142.3( 2

2

23.204 cm

cml 8

2

rrl


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SURFACE AREA OF SPHERE

Surface area of a sphere =24 r

Where r is the radius of the sphere


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Example:

Find the surface area of the sphere.

(Take )7

22


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SOLUTION

Surface area of the sphere:

2221545.3

7

2244 cmr


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POP QUIZ


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1) Find the surface area of the sphere

that has

a) radius =

b) diameter =

m11

31

cm8.2


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SOLUTION

a)

b) Diameter =

1131r

2

2

11

14

7

2244

r 3636.20

82.2

22 )2

8.2(

7

2244 r 64.24


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2) Find the value of for the solid

shown in the diagram if its surfacearea is 1551 .

Take

h

2cm

7

22

21 cm

h cm


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SOLUTION

The solid given is cylinder.221r ?h

155122 2 rhr

15512

21

7

222

2

21

7

222

2

h

155166693 h

85866 h

13h


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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


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SOLUTION

Diameter =14 cm 7r ?l

2862 rrl

28677

227

7

22 2

s

28615422 s

13222 l

6l


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4) A sphere has a surface area of .

What is its radius?

2

7

4804 mm


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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


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5) Calculate the value of for the

following solid.

x

10 cm

x cm

Surface area = 785 cm2


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SOLUTION

10r

785107

2210

7

22 22

lrrl

7857

2200

7

220l

7

3295

7

220l

97.14l


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6)

12 cm

5 cm

Calculate the surface area of the cone


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Solution

13 cm12 cm

5 cm

Surface area = 282.8571


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7)2.8 mm

If the diameter of the iron rod is 2.8 mm and thesurface area of the rod is 2.8mm, find its length.


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Solution

4.1r

32.8924.17

2224.1

7

22222

22

hrrh

32.89832.128.8 h

100h


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Example 1

Find the total surface area of the

following solid. Take .3.142


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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 . 3.142

Hemi

means half.

Example 2


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Ex12.3A, Ex12.3B, Ex12.3C

HOMEWORK

NEXT LESSON Chapter 13 - Statistics

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Solid Geometry II - Slide