volume and surface area grade 9.notebook
volume and surface area grade 9.notebook
December 06, 2011
Determine the Area of the following shapes 15 c
m
12 cm
Determine the area of brick needed to face this bridge. 35 m
8 m
10 m
10 m
1
volume and surface area grade 9.notebook
December 06, 2011
VOLUME & SURFACE AREA Curricular Expectations: • develop through investigation the formulas for Volume of a pyramid, cone and sphere • determine through investigation that the surface area of a square based pyramid is the same as finding area of 4 equal triangles plus the area of the square base • solve problems involving SA & Vol of PRISMS, PYRAMIDS, CYLINDERS, CONES & SPHERES including COMPOSITE figures
2
volume and surface area grade 9.notebook
December 06, 2011
VOLUMES
WHAT IS A PRISM
http://youtu.be/TM004YsdvLQ http://youtu.be/aLyQddyY8ik
calculus explaination of volume of sphere
http://youtu.be/xuPl_8o_j7k
surface area of PRISMS
http://youtu.be/mL7E_NBhyIw surface area of cylinder
http://youtu.be/GpHhvuRbB8
SURFACE AREA PRYAMID & CYLINDER
http://youtu.be/ajobBlMVwjA
3
volume and surface area grade 9.notebook
December 06, 2011
TERMS to know: VOLUME: amount of space an object occupies • measured in CUBIC units
SURFACE AREA: number of square units needed to cover the surface of a 3-D object
PRISM: a 3-D object with 2 parallel congruent bases. • named by the shape of its base
PYRAMID: base is a polygon, and other faces are TRIANGLES that meet at a common VERTEX
LATERAL FACES : the faces of a Prism or Pyramid that are NOT BASES Lateral Face
Base
SLANT HEIGHT: on a Pyramid, it is the height of the lateral face slant height
4
volume and surface area grade 9.notebook
December 06, 2011
What is shape of Base? Write the formula for its AREA
What is shape of each lateral face? Write formula for its area (mark out on each shape, the dimensions required to find the area)
Volume of the Pyramid: Which Dimensions do you need to know in order to determine the Volume of this Pyramid? How is the height of the Pyramid different from the "height" (slant height) of each triangle.
THINKING: if you were given the slant height, how could you determine the HEIGHT of the pyramid, in order to find the Volume.
5
volume and surface area grade 9.notebook
December 06, 2011
VOLUME OF PRISMS: V = area of base x third dimension (depth or height) shape
6
volume and surface area grade 9.notebook
December 06, 2011
VOLUME OF PYRAMIDS & CONES:
7
volume and surface area grade 9.notebook
December 06, 2011
Determine the Volumes of the following shapes
12 cm
18 cm
5
cm
8 cm
10 cm
15 cm
12 cm
10
cm
m
8 c
1.5 m
2 m
25 cm
3 m
18 cm
12 cm
10 cm
10
4 16
8
8
volume and surface area grade 9.notebook
December 06, 2011
V = area of rect. base X height of pyramid 3 12 cm
18 cm
15 cm
12 cm
10 cm
m
8 c
9
volume and surface area grade 9.notebook
1.5 m
December 06, 2011
Triangular Based Prism
of prism
length 2 m
3 m
V = area of triangle base X length of prism or
10
volume and surface area grade 9.notebook
December 06, 2011
V = area of circular base X height of cylinder 25 cm
10 cm
V = area of circular base X height of cone 3 18 cm
12 cm
V = area of hexagonal base X depth of prism 10
Note: the hexagon is 2 trapezoids ∴ find area of 1 trapezoid and multiply by 2
4 16
8
this is area of trap. base only-not the volume.....
11
volume and surface area grade 9.notebook
December 06, 2011
Draw the nets of the following shapes, label the dimensions. b) Calculate any required dimensions that are missing to calculate the Surface Area of each shape. c) Calculate the Surface Area of each shape Show all your work
6 cm
cm
8
15 cm
12
volume and surface area grade 9.notebook
December 06, 2011
the missing length is NOT NEEDED FOR AREA OF TRIANGLE but for area of RECTANGULAR SIDES it is the SLANT HEIGHT of the triangular face the HYPOTENUSE
10
sin mis
g sin
mis g missing
missing
8
60 cm
60 cm
60 cm
60 cm
this is HEIGHT of triangle
8 missing
ng mi ssi
mis
g sin
missing
13
volume and surface area grade 9.notebook
December 06, 2011
surface area of cone http://youtu.be/6AqTX1iB8OQ
surface area of CONE & SPHERE
14
volume and surface area grade 9.notebook
December 06, 2011
EIG T H
AN
SL
s is
SURFACE AREA of CONES HT
SA of cone = Area circular base + Area Lateral surface s i s S
LA
NT
H
EI
GH T
Determine the VOLUME and SURFACE area of the CONE below
V = area of circular base X height of cone 3 You do NOT need Slant Height to determine the VOLUME of a Cone
conical fulstrum http://youtu.be/5tPMvXYPzHc
15
volume and surface area grade 9.notebook
December 06, 2011
PYRAMIDS
ht eig
nt H
Sla
Height of Pyramid
Slant Height
SA = Area of Base of Pyramid + Total Area of Lateral Faces
where h is the slant height s where 'l' is also the base of the triangle -so call length of the square 'b'
16
volume and surface area grade 9.notebook
December 06, 2011
SPHERE -- surface area & Volume
Determine the RADIUS of a ball that has a Surface Area of 215cm2
17
December 06, 2011
Determine the Area of the following shapes 15 c
m
12 cm
Determine the area of brick needed to face this bridge. 35 m
8 m
10 m
10 m
1
volume and surface area grade 9.notebook
December 06, 2011
VOLUME & SURFACE AREA Curricular Expectations: • develop through investigation the formulas for Volume of a pyramid, cone and sphere • determine through investigation that the surface area of a square based pyramid is the same as finding area of 4 equal triangles plus the area of the square base • solve problems involving SA & Vol of PRISMS, PYRAMIDS, CYLINDERS, CONES & SPHERES including COMPOSITE figures
2
volume and surface area grade 9.notebook
December 06, 2011
VOLUMES
WHAT IS A PRISM
http://youtu.be/TM004YsdvLQ http://youtu.be/aLyQddyY8ik
calculus explaination of volume of sphere
http://youtu.be/xuPl_8o_j7k
surface area of PRISMS
http://youtu.be/mL7E_NBhyIw surface area of cylinder
http://youtu.be/GpHhvuRbB8
SURFACE AREA PRYAMID & CYLINDER
http://youtu.be/ajobBlMVwjA
3
volume and surface area grade 9.notebook
December 06, 2011
TERMS to know: VOLUME: amount of space an object occupies • measured in CUBIC units
SURFACE AREA: number of square units needed to cover the surface of a 3-D object
PRISM: a 3-D object with 2 parallel congruent bases. • named by the shape of its base
PYRAMID: base is a polygon, and other faces are TRIANGLES that meet at a common VERTEX
LATERAL FACES : the faces of a Prism or Pyramid that are NOT BASES Lateral Face
Base
SLANT HEIGHT: on a Pyramid, it is the height of the lateral face slant height
4
volume and surface area grade 9.notebook
December 06, 2011
What is shape of Base? Write the formula for its AREA
What is shape of each lateral face? Write formula for its area (mark out on each shape, the dimensions required to find the area)
Volume of the Pyramid: Which Dimensions do you need to know in order to determine the Volume of this Pyramid? How is the height of the Pyramid different from the "height" (slant height) of each triangle.
THINKING: if you were given the slant height, how could you determine the HEIGHT of the pyramid, in order to find the Volume.
5
volume and surface area grade 9.notebook
December 06, 2011
VOLUME OF PRISMS: V = area of base x third dimension (depth or height) shape
6
volume and surface area grade 9.notebook
December 06, 2011
VOLUME OF PYRAMIDS & CONES:
7
volume and surface area grade 9.notebook
December 06, 2011
Determine the Volumes of the following shapes
12 cm
18 cm
5
cm
8 cm
10 cm
15 cm
12 cm
10
cm
m
8 c
1.5 m
2 m
25 cm
3 m
18 cm
12 cm
10 cm
10
4 16
8
8
volume and surface area grade 9.notebook
December 06, 2011
V = area of rect. base X height of pyramid 3 12 cm
18 cm
15 cm
12 cm
10 cm
m
8 c
9
volume and surface area grade 9.notebook
1.5 m
December 06, 2011
Triangular Based Prism
of prism
length 2 m
3 m
V = area of triangle base X length of prism or
10
volume and surface area grade 9.notebook
December 06, 2011
V = area of circular base X height of cylinder 25 cm
10 cm
V = area of circular base X height of cone 3 18 cm
12 cm
V = area of hexagonal base X depth of prism 10
Note: the hexagon is 2 trapezoids ∴ find area of 1 trapezoid and multiply by 2
4 16
8
this is area of trap. base only-not the volume.....
11
volume and surface area grade 9.notebook
December 06, 2011
Draw the nets of the following shapes, label the dimensions. b) Calculate any required dimensions that are missing to calculate the Surface Area of each shape. c) Calculate the Surface Area of each shape Show all your work
6 cm
cm
8
15 cm
12
volume and surface area grade 9.notebook
December 06, 2011
the missing length is NOT NEEDED FOR AREA OF TRIANGLE but for area of RECTANGULAR SIDES it is the SLANT HEIGHT of the triangular face the HYPOTENUSE
10
sin mis
g sin
mis g missing
missing
8
60 cm
60 cm
60 cm
60 cm
this is HEIGHT of triangle
8 missing
ng mi ssi
mis
g sin
missing
13
volume and surface area grade 9.notebook
December 06, 2011
surface area of cone http://youtu.be/6AqTX1iB8OQ
surface area of CONE & SPHERE
14
volume and surface area grade 9.notebook
December 06, 2011
EIG T H
AN
SL
s is
SURFACE AREA of CONES HT
SA of cone = Area circular base + Area Lateral surface s i s S
LA
NT
H
EI
GH T
Determine the VOLUME and SURFACE area of the CONE below
V = area of circular base X height of cone 3 You do NOT need Slant Height to determine the VOLUME of a Cone
conical fulstrum http://youtu.be/5tPMvXYPzHc
15
volume and surface area grade 9.notebook
December 06, 2011
PYRAMIDS
ht eig
nt H
Sla
Height of Pyramid
Slant Height
SA = Area of Base of Pyramid + Total Area of Lateral Faces
where h is the slant height s where 'l' is also the base of the triangle -so call length of the square 'b'
16
volume and surface area grade 9.notebook
December 06, 2011
SPHERE -- surface area & Volume
Determine the RADIUS of a ball that has a Surface Area of 215cm2
17
