mat2793 - volume of composite shapes

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