mat2793 - volume of composite shapes
TRANSCRIPT
Volume of Composite Shapes
Cylinder Cone
𝑽=𝝅 𝒓𝟐𝒉 𝑽=𝟏𝟑𝛑𝒓𝟐𝒉
Sphere
𝑽=𝟒𝟑𝝅𝒓𝟑
Basic shapes & their volumes
Basic shapes & their volumes
𝑽=(𝟔 ) 𝟏𝟐𝒃𝒂𝒉
Hexagonal Prism
𝑽=𝟏𝟐𝒃𝒂𝒉 𝑽=
𝟏𝟑𝒍𝒘𝒉
Triangular Prism
Rectangular Pyramid
What is a composite shape?
Two basic shapes added together
is a triangular
prism
on top of arectangular
prism
This house
Two basic shapes added together
is a triangular
prism
on top of arectangular
prism
This house
This hexagonal prism becomes a
nut
One shape subtracted from another
This hexagonal prism becomes a
nut
by removing a cylinder from its center
One shape subtracted from another
A shape that is truncated (sliced)
This cup
A shape that is truncated (sliced)
is a large cone
with a small cone removed
This cup
A shape that is truncated (sliced)
is a large cone
with a small cone removed
This cup
A shape that is truncated (sliced)
is a large cone
with a small cone removed
This cup
A closer look at adding shapes
Warm-up: Can you identify the basic shapes in the following examples?
Example - Ice cream cone
Example - Ice cream cone
hemisphere( sphere)
cone
Example - Ice cream cone
hemisphere( sphere)
cone
Example - Ice cream cone
hemisphere( sphere)
cone
Example - Traffic cone
Example - Traffic cone
cone
rectangular prism
Example - Traffic cone
cone
rectangular prism
Example - Traffic cone
cone
rectangular prism
Example – Washington Monument
Example – Washington Monumentpyramid
rectangularprism
Example – Washington Monumentpyramid
rectangularprism
Example – Washington Monumentpyramid
rectangularprism
Example - Hopper bin
Example - Hopper bin
cylinder cones
Example - Hopper bin
cylinder cones
Example - Hopper bin
cylinder cones
Finding the volume of a composite object using addition
ExampleSarah wanted to fumigate her shed for ants. If one can of spray will treat 600 cubic feet, how many cans will she need for her shed?
7 ft
8 ft
10 ft
V = triangular prism + rectangular prism
2.5 ft
ExampleSarah wanted to fumigate her shed for ants. If one can of spray will treat 600 cubic feet, how many cans will she need for her shed?
7 ft
8 ft
10 ft
V=12bah + lwh
V = triangular prism + rectangular prism
2.5 ft
ExampleSarah wanted to fumigate her shed for ants. If one can of spray will treat 600 cubic feet, how many cans will she need for her shed?
7 ft
8 ft
10 ft
V=12bah + lwh
V = triangular prism + rectangular prism
V =12
(8 ) (2.5 ) (10 ) + (10 ) (8 ) (7 )
2.5 ft
ExampleSarah wanted to fumigate her shed for ants. If one can of spray will treat 600 cubic feet, how many cans will she need for her shed?
7 ft
8 ft
10 ft
V=12bah + lwh
V = triangular prism + rectangular prism
V =12
(8 ) (2.5 ) (10 ) + (10 ) (8 ) (7 )
ft3
2.5 ft
ExampleSarah wanted to fumigate her shed for ants. If one can of spray will treat 600 cubic feet, how many cans will she need for her shed?
7 ft
8 ft
10 ft
V=12bah + lwh
V = triangular prism + rectangular prism
V =12
(8 ) (2.5 ) (10 ) + (10 ) (8 ) (7 )
ft3
Sarah will need two cans of spray.
2.5 ft
Summary
Identify shapes involved
Identify formulae required
Add formulae to find composite
volume
Clearly indicate final answer with appropriate units
IMAGE CREDITS
ShutterstockBow Valley College